Theo van Doesburg actually wanted to call the magazine 'The Straight Line', but influenced by the other members the name became 'The Style' after all. The members thought that the word 'Style', preceded by the the word 'The' , suggests that it is the best, possibly even the only style, usable in the modern art and society. 

The principals of The Style;
The Style is a variation of the abstract art, witch is characteristic for the
opinions about art of the modern times. This modern art had to be
 non-illustrative and non-telling in contrast to the former art movements and
 it's opinions. The modern art had to be able to stand on its own and had to be
 understandable without referring to the concrete world. So it did not have to
 reflect something identifiable to be understandable. 
 The Style is recognizable by the use of straight horizontal and vertical lines
as well as the use of the primary colors red, yellow and blue. They also used
 the colors black, white and gray. The result of it all seems an almost
 technically constructured totality. It was not the intention to tell something
 concrete, but to show the world the ideal harmony.

 The Style went back to the fundamental elements of the art: color and form, level and line. With these elements the artist developed new sculptural language and with that the placed the ideal world opposite the reality. Most of the artist used closed and open forms, density and space, color and form. By using these elements within one painting, the ideal harmony could be reached. All elements have their own function in the totality. 

 The lines are the borders and make the open or closed forms. The lines are also used to create a certain space. The border of the painting is not the end of the painting. We can use our fantasy to fill in the rest; to let it grow as big  as we want, as big as we can imagine.  By using only the primary colors, the artist could create a 3-dimensional effect. The colors attract immediate attention. Therefor the rest of the painting seems to go to the background. It  looks like the white forms are further back than the colored forms. That is how the artists created a front and a back in their paintings, witch is held in harmony because of the  use of
different sized forms. So the ideal harmony could only be reached by using the perfect proportion between: the size of the colored forms ; the colored and uncolored forms the closed and open forms. By the use of ideal proportions, the artists were able to create peace and balance in their work, witch reflects the ideal harmony in the most perfect way.  The members of the alliance saw art as the bridge between reality and harmony. If harmony was reached in reality, art would lose its function." (culled directly from, http://www.the-artfile.com/uk/styles/stijl/stijl.htm)

Piet Mondrian. Broadway Boogie-Woogie. 1942–43.
Oil on canvas, 50 x 50" (127 x 127 cm).
The Museum of Modern Art, New York. 
Given anonymously.
Photograph ©1997 The Museum of Modern Art, New York.
Abstract Formalism or International Style or de Stijl

Iconography: Eliminating the real and visible from his paintings, he extracted pure form and color from the objective world. His aesthetic philosophy is, unsurprisingly, as distilled as his paintings: "What do I want to express with my work? Nothing else than that which every other artist seeks: to achieve harmony through the balance of the relationships between lines, colors, and planes. But only in the clearest and strongest way." Mondrian never viewed the black lines as edges: they weren't meant to contain the colors, since doing so would create foreground and background and thus interfere with the total unity of the work. Instead, the lines moved through the rectangles of color while remaining independent of them. Overtly basic compositions of color and line, these paintings emphasize the dynamic interaction of the essential elements of form and color.
 

Context:  According to www.artandculture.com,"The members of the De Stijl movement were pious, self-effacing artists bent on creating pure and accessible art. Although the Dutch painter Piet Mondrian did not himself organize the groups with which he is associated -- De Stijl, Cercle et Carré (Circle and Square), and Abstraction-Création -- his participation was essential to the growth of abstraction. 

Early in his career Mondrian worked in the naturalist style, but moved slowly toward innovations in color and abstraction. From the Impressionist and Pointillist-style landscapes and still lifes, composed around 1906, Mondrian’s aesthetic quickly evolved into free, Fauvist-style landscapes. A 1909 Amsterdam exhibition of these raw landscapes was fiercely criticized, but Mondrian continued to develop his style with an eye toward innovation. By 1911, he had moved to Paris and launched himself into Cubism. 
Mondrian's shift toward greater abstraction was inspired by a desire to express universals.  

Van Doesburg and Mondrian were the theoretical engines behind De Stijl, whose artists strove for anonymity and envisioned a collective art.  For Mondrian, the tensions between modern technology and individuality were more a matter of perception than reality, and he believed that the move from the particular to the abstract was the way to bring together these two apparent opposites. Mondrian composed his first plus-minus compositions -- paintings with rhythmic horizontal and vertical lines -- in 1917, and by 1918 he had created his first geometric grid works. But it was not until 1920, after the publication of his treatise "Le Neo Plasticisme" (Neo-Plasticism), that he composed the first heavily black-outlined colored rectangles.  In 1921, Mondrian further reduced his palette to three pure primary colors plus black, white, and gray. After his 1940 emigration to New York, the painter made his final stylistic refinement, changing to a framework of black lines replaced by colored lines and rows of small colorful rectangles. "Broadway Boogie Woogie," painted just prior to Mondrian’s death in 1944, created a splash, serving as a catalyst for the American abstractionists of the ‘50s and ‘60s."

- From David Sylvester, "About Modern Art: Critical Essays, 1948-1997"
- Taken from www.artchive.com 

Theo van Doesburg 
[Color contruction in the 4th dimension of space-time] 1924
Abstract Formalism or International Style or de Stijl

Iconography: This is an example of a work done in the form of the group of artists who ascribed to the 'De Stijl". It is using the elements of horizontal and vertical, black and white, and primary colors. It is abstraction distilled down to its' most basic. Note, however, that it is intentionally not perfect. What the artist wants the viewer to realize is that the longer it is looked at, the more one can see. The lines are of varying widths, and in some cases do not follow all the way to the edge of the canvas. The colors are not consistent all the way through, if one looks closely, they begin to pick up the differences in shade and values. It can be seen as well in the lower work that the color values shift constantly, and though it may, at first glance, seem to be more complicated than the top composition, it is just as basic and abstract. The only difference being the creation of a three-dimensional illusion made by overlapping objects.

Context: "Christian Emil Marie Küpper, who adopted the pseudonym Theo van Doesburg, was born in Utrecht, the Netherlands, on August 30, 1883. His first exhibition of paintings was held in 1908 in the Hague. In the early 1910s he wrote poetry and established himself as an art critic. From 1914 to 1916 van Doesburg served in the Dutch army, after which time he settled in Leiden and began his collaboration with the architects J. J. P. Oud and Jan Wils. In 1917 they founded the group De Stijl [more] and the periodical of the same name; other original members were Vilmos Huszár, Piet Mondrian, Bart van der Leck, and Georges Vantongerloo. Van Doesburg executed decorations for Oud’s De Vonk project in Noordwijkerhout in 1917.  In 1920 he resumed his writing, using the pen name I. K. Bonset and later Aldo Camini. Van Doesburg visited Berlin and Weimar in 1921 and the following year taught at the Weimar Bauhaus [more], where he associated with Raoul Hausmann, Le Corbusier, Ludwig Mies van der Rohe, and Hans Richter. He was interested in Dada [more] at this time and worked with Kurt Schwitters as well as Jean Arp, Tristan Tzara, and others on the review Mécano in 1922. Exhibitions of the architectural designs of Gerrit Rietveld, van Doesburg, and Cor van Eesteren were held in Paris in 1923 at Léonce Rosenberg’s Galerie l’Effort Moderne and in 1924 at the Ecole Spéciale d’Architecture.The Landesmuseum of Weimar presented a solo show of van Doesburg’s work in 1924. That same year he lectured on modern literature in Prague, Vienna, and Hannover, and the Bauhaus published his Grundbegriffe der neuen gestaltenden Kunst (Principles of Neo-Plastic Art). A new phase of De Stijl was declared by van Doesburg in his manifesto of “Elementarism,” published in 1926. During that year he collaborated with Arp and Sophie Taeuber-Arp on the decoration of the restaurant-cabaret L’Aubette in Strasbourg. Van Doesburg returned to Paris in 1929 and began working on a house at Meudon-Val-Fleury with van Eesteren. Also in that year he published the first  issue of Art concret, the organ of the Paris-based group of the same name. Van Doesburg was the moving force behind the formation of the group Abstraction-Création in Paris. The artist died on March 7, 1931, in Davos, Switzerland." (www.guggenheim.org)

Iconography: It can be seen from this study how the essence of DeStijl was at work. Many right angles and cube forms, black and white and primary colors, and simplicity. 

Context: Rietveld was a part of the movement, in the form of architecture. Whlie Mondrian and vanDoesburg were traditionally painters, Rietveld was a cabinet maker and a carpenter. He brought the conceptual ideas of DeStijl to life in three dimensional form.

Gerrit Rietveld. Schroder House 1924
Utrecht, Netherlands
Weightless Floating Walls
Abstract Formalism or International Style or de Stijl

 
 

Iconography: "Gerrit Rietveld worked closely in collaboration with the client for this house.  More than any other, this is either—in Banham's words—'a cardboard Mondrian' or an enormous piece of furniture masquerading as a house. All windows could only be opened up completely, at right angles to frames, repeating the devices by which the upper floor could be transformed from one single space into a series of smaller ones—the point being that in either positioning of windows or moveable walls, the house retained its neoplastic hypothesis."
 —David Dunster. Key Buildings of the Twentieth Century Volume 1: Houses 1900-1944. p24.
"Reaction to the house is best described as polar, either people loved or hated the house. In many senses this is what Truss Schröder wanted, to challenge peoples traditional views. Most of the neighbours didn't like the house as many would stand waiting for the house to fall over, due to its radical construction. Even today many people find its direct modernity alarming. Sometimes the children were subjected to mocking because they lived in a "looney house". (Overy, 1988, p78)  Rietveld's peers (especially Van Doesburg) praised the house in terms of its achievement of De Stijl plastic principles of architecture. Other professional peers such as
Oud publicly denounced the building as harmful to modern architecture; stating that it was lacking solidity; was prone to wear and tear and would age badly . (Overy,1988, p79) Privately Oud held the house in high regard as an achievement ahead of its time. By the 1950's the Schröder house became entrenched as one the greatest developments of modernism as it was the first open-plan house. Up until the Schröder house Western architecture had been "enclosed". Rietveld however considered architecture as giving rhythm to a corporeal experience of space which is connected to "total space". Rietveld stated that the aim of his architecture was to "preserve a free, light and unbroken space, that gives clarity to our lives and contributes a new sense of life". (Kuper, 1992, p39)  As a spatial theory Rietveld considered architecture as manifestation of a specific visual form transcending the particular human activity it housed. Rietveld's reinterpretation of design was forged in the context of practical, pre-aesthetic requirements - that the building must provide functional and economic delineation of space. (Buffinga, 1971, p5) This Functionalism was enunciated by Rietveld as "eliminating everything that is superfluous. This is also what the word means in a social sense: it is a sort of spatial hygiene." (Kuper, 1992, p36) The expression of this Functional architecture is related to the idea of "befreites wohnen" meaning free or independent living.Rietveld's background in furniture design served as the main basis from which the conceptual functional and aesthetic issues and his attitude to design were to shape the design of the house. In many ways the furniture (such as the red blue chair, 1922) and the Schröder house were parallel. Rietveld once said :... when I got a chance to make a house based on the same principles as that (Red Blue - ed) chair, I seized it eagerly." (Overy, 1988, p61) The Schröder house was also the first truly open plan house (with the movable partitions on the first floor). It was from this manifestation of continuous space that the house gave modernism the greatest freedom from the previously enclosed nature of a house. The concept was more than just a liberation of the plan from structure (such as Le Corbusier's plan libre) it was conscious effort to elevate architecture to a realm where space and function were integral components. Many of Rietveld's
spatial devices and organisational methods can be traced throughout the canons of modernism, such as Mies Van der Rohe and Frank Lloyd Wright. The project was a manifestation of Rietveld's ideas about housing and living. He perceived traditional housing as a neutral space in which inhabitants conformed to the passive environment. (Kuper, 1992, p100). Rietveld considered that architects had a shallow conception of the specific requirements of housing and lifestyle. all too often Architects reproduced generic housing types without considering the relationship between house owner and lifestyle, instead developing housing that had degenerated into automatism. According to Rietveld inhabiting a house must be conscious act, carefully tailored to the needs of the inhabitants. (Kuper, 1992, p100) Truus Schröder's conceived new life-style was celebrated as a work of art (reinforced through the environment) with the house providing a setting for a masque celebrating the act of living. (Overy, 1988, p22) Daily routines were emphasised by creating specially designed fittings and built-in furniture, connecting the activities conclusively to the principles of the architecture.Adaptability became the key link within the whole house. During the day, walls are rolled away so that bedrooms merge into one living space. Also room size related to time spent in them and the activity, and activity spaces were merged such as the dining room with the kitchen, and the corridor with the staircase. Just as Rietveld's Red Blue chair is a proclamation of sitting down ("sitting is a verb" is Rietveld's famous remark), similarly the Schröder house is a manifestation of an enlightened and active living. (Kuper, 1992, p100) 
Rietveld instead of imitating nature with ornamentation sought to establish an interaction between house and nature. Space and material were conceived in relation to
revealing reality; as nature and culture are fused by achieving a symbiosis between outside and inside spatial realms. (Overy, 1988, p27) The perception of nature
through the open transition zones provide a discernible contrasting link; between the primary colours of the house and the assemblage of colours of the adjacent park; the
plain smooth geometric and proportioned planes and the unstructured organic forms. (Overy, 1988, p27)" (Full text at, http://Sander.vanZoest.com/schroder-2.html)
 

Context:  "No one had ever looked at this little lane before this house was built here. There was a dirty crumbling wall with weeds growing in front of it. Over there was a small farm. It was a very rural spot, and this sort of fitted in. It was a deserted place, where anyone who wanted to pee just did it against this wall. It was a real piece of no-man's-land. And we said, 'Yes, this is just right, let's build it here.' And we took this plot of ground and made it into a place with a reality of its own. It didn't matter what it was, so long as something was there, something clear. And that's what it became. And that's always been my main aim: to give to a yet unformed space, a certain meaning."
 —Gerrit Rietveld. from Paul Overy, Lenneke Büller, Frank den Oudsten, Bertus Mulder. The Rietveld Schroder House. p52.
 "...We didn't avoid older styles because they were ugly, or because we couldn't reproduce them, but because our own times demanded their own form, I mean, their own manifestation. It was of course extremely difficult to achieve all this in spite of the building regulations and that's why the interior of the downstairs part of the house is somewhat traditional, I mean with fixed walls. But upstairs we simply called it and 'attic' and that's where we actually made the house we wanted."
 —Gerrit Rietveld. from Paul Overy, Lenneke Büller, Frank den Oudsten, Bertus Mulder. The Rietveld Schroder House. p73.
(www.greatbuildings.com)

"The famous Red & Blue chair was designed in 1917. Nothing has existed like that before. It marked the transition between the organic, curving Art Noveau Style and the crisp, chic Art Deco. The Red & Blue chair is composed out of a dramatic interplay of straight lines to form patterns. The lines produce form by enclosing space, the structure has very simple components and the striking colors are a reminder of paintings by the artist Mondrian. Although there is no upholstery, the chair is amazingly comfortable."  www.dezignare.com

Context: This chair, or rather the duplicates of it, are still being sold today. It has become increasingly popular as a symbol of DeStijl, perhaps a testament to the thought that this movement may never truly die out. As said on www.centraalmuseum.com, "With the Red-and-Blue Chair, Rietveld reduced the armchair to its most elementary form. In 1918, he strove to create a chair without volume or mass, one that left surrounding space unbroken. Rietveld also wanted to make furniture that could be machine-produced. The famous colour scheme probably only dated from around 1923, the colours adding to the strength of the spatial character of the work. The superficial similarity to the work of Mondrian made the Red-and-Blue Chair an icon of De Stijl design. Rietveld himself attached no absolute value whatever to the primary colours, making the same chair for Charley Toorop in pink and sea-green, as well as a version for Paul Citroen in black with white trim on the crosscuts."