These references may be of assistance.
Mikrokosmos, progressive pieces (153) for piano in 6 volumes, Sz. 107, BB 105https://www.allmusic.com/composition/mikrokosmos-progressive-pieces-153-for-piano-in-6-volumes-sz-107-bb-105-mc0002361203“Mikrokosmos was originally designed as a collection of pieces for the beginning pianist, but over time it took on grander proportions, comprising 153 individual pieces that spanned the range of technical difficulty. Dividing into six volumes, it begins with pieces for beginners and progresses to those that challenge even the most accomplished pianist. That Mikrokosmos has become a viable progressive method is demonstrated by its ubiquity in the repertories of modern piano students, but its reputation rests on more than its technical and pedagogical applications; Bartók's work represents a varied and finely crafted catalog of twentieth century musical idioms. In Bartók's own words, it "appears as a synthesis of all the musical and technical problems which were treated and in some case only partially solved in the previous piano works." Perhaps chief among these musical problems was Bartók's attempted synthesis of Eastern and Western European musical traditions, particularly Eastern folk music with the Germanic tradition (as represented by Bach and Beethoven) and with the progressive harmonies of Claude Debussy.
The first 66 pieces in Mikrokosmos (Vols. 1 and 2) are dedicated to Bartók's son, Peter, for whose use they were originally intended. Many of these pieces are technical exercises, useful for developing finger and hand independence, as well as hand span; however, they are also of interest for their musical language. Hungarian folk tunes, pentatonic, whole-tone and modal harmonies, as well as more adventurous octatonic chromatic scales all form the basis for these short pieces.
Volumes 3 and 4 make up numbers 67 through 121. These pieces display increased harmonic complexity and technical demands. Bartók employs more polymodes (the use of different modes, or keys, simultaneously), along with octatonic and diatonic scale fragments to construct these pieces. The compositions in the third and fourth volumes are also important because they betray the influence of Franz Liszt, particularly in terms of tone color; Bartók wrote of his desire, in these pieces, to "poetically color the piano tone."
The final volumes (5 and 6) of the Mikrokosmos were intended as concert pieces for professional pianists. They differ from the preceding pieces in many respects: their contrapuntal texture is more dense (four parts), the melodic and harmonic material is more characteristic of Bartók's non-pedagogical works, and rhythmic structures are much more complicated and include vigorous syncopations and Bulgarian dance rhythms.
While Bartók's intention to synthesize Bach, Beethoven, and Debussy was perhaps not fully realized, Mikrokosmos nonetheless compares well with some of Bach and Debussy's ostensibly pedagogical keyboard works. Like Bach's Inventions or Debussy's Études, for example, Mikrokosmos is not merely a work of practical value, but also a work of art with much purely musical substance.”
Béla Bartók's Pedagogical Legacy: Mikrokosmoshttps://www.ispci.timofeev.org/index.php?option=com_content&view=article&id=218&Itemid=227&showall=1 Bartók's publisher wrote:
“I could speak only from my own pianistic experience: from J. S. Bach to the Romantics every stylistic period had its educational literature which taught the beginner about both musical style and its technical problems; after Schumann this up-to-date literature of exercises and easy pieces began to disappear and the young player still had to start and finish with Czerny, which gave him all the equipment for Mozart and Beethoven but was no help with Chopin and Brahms, let alone what followed. ‘But I am always writing short, easy pieces for beginners,' replied Bartók, ‘I have drawers full of them.' This was not enough, I said. What was required was a system, a method....Bartók listened attentively and said he would think it over. The result was his Mikrokosmos, which I published in London in 1940.”Other quotes:
“Studying pieces from Mikrokosmos provides a foundation for the student's comprehension of early 20th-century music. For those who have been trained solely in western diatonic methods, Mikrokosmos takes them to such unfamiliar places as unpredictable tonalities and phrases of irregular length. It also develops the aural facility to comprehend modal and polytonal music. Renowned piano pedagogue Ylda Novik found that incorporating Mikrokosmos into piano study cultivates an appreciation for contemporary music in students:
One of the most exciting elements of Mikrokosmos, its use of modality, exposes the student to the full gamut of tonal combinations made possible by utilization of modes. Through modal writing, the student is introduced to broader ways of tonal thinking, expanding even to polytonality and atonality.... The children who study Mikrokosmos along with folk tunes, and, later, the simple classics, accept it as readily as the rest of their curriculum. It is no surprise that very often their preference is for Bartók over much other material.”
“Bartók prefaces the first three volumes with an explanation of how Mikrokosmos deviates from a traditional method, in that
"technical and theoretical instructions have been omitted, in the belief that these are more appropriately left for the teacher to explain to the student." This departure from Piano Method allows the teacher flexibility to provide students with individual direction, which Bartók encourages in the preface to Volume One:
"The pieces and exercises are arranged in progressive order according to the technical and musical difficulty. However, teachers may alter this order in accordance with the ability of the pupil.”
“Mikrokosmos fills an important pedagogical need and prepares students to play music of the 20th century. Its insightful application of various hand positions, time signatures, and rhythmic syncopations familiarizes beginners with many technical aspects of piano playing. The folk qualities present in its melodies, which informed all of Bartók's compositions, accustom students to the many modal and dissonant elements that permeate so much of contemporary music. Through the study of Mikrokosmos, beginning students will experience the "small world" of the piano-playing art.”
This essay goes into some detail about the skills taught in the various pieces.
I started teaching myself piano a few months ago and Mikrokosmos is one of my resources. I learn the pieces in order. When I’m able to play a piece 3 times in succession at the specified tempo, I move on to the next one.
If you enjoy and aspire to play modern classical music, especially music inspired by a variety of folk styles such as that composed by Bartók, I know of no other set of etudes that are likely to provide better preparation.