[1] He trained at the Moscow School of Painting, Sculpture and Architecture (1873–1874), with Vladimir Sherwood on the construction site of State Historical Museum (1875–1877), and at the Imperial Academy of Arts (1877–1882), winning a study tour to Italy and France (1883–1884), where he assisted Charles Garnier in preparation to the Exposition Universelle (1889).

His knowledge of Greek and Byzantine classics was evident, however, the University also wanted perfection in other historical interiors (Egyptian, Babylonian) and sent Klein on two overseas study tours (1897, 1899–1900).

Klein had studied the latest forms of museum construction in Europe, and he built a temple to the arts that expressed civic pride and private patronage, thus pleasing his benefactor, Nechaev-Maltsov, and creating what Lukomskii would have called approvingly a "European" building, noticeably different from the public and commercial buildings whose neoclassicism derived from the local Empire style.

Klein employed Vladimir Shukhov for structural engineering of ceilings and sunroofs, Ivan Rerberg and other younger architects.

Modern critics place Klein's talent below his contemporaries like Fyodor Schechtel or Lev Kekushev (Maria Naschokina, p. 255).

Klein had his limitations, but his immense academic background and drawing skills allowed him to imitate styles like Victorian architecture or Russian Revival.

He advocated "finding out the unique, individual features of a trainee architect, and bringing up his own creative conscience" ("выявление индивидуальности проектирующего ... и в воспитании в нем художественного самосознания", Maria Naschokina, p. 257), and promoted the French model of architectural workshops.