[Another answer contains this suggestion, but it's at the end of the answer and no details are given.]

I would rather like to read Kostrikin's *Introduction to Algebra* (the 2nd edition, published in 2000: Кострикин – *Введение в алгебру*). It is in 3 volumes: 'Basic algebra', 'Linear algebra', and 'Fundamental structures of algebra'. Approximately, they cover:

I – preliminaries, matrices & determinants, basics of groups rings & fields, complex & real polynomials

II – vector spaces & linear operators, euclidean hermitian affine & projective spaces, tensors

III – structures of various groups, basic representation theory, rings modules & algebras, Galois theory

The book begins with a discussion about what algebra is, a historical overview, and a set of substantial problems that can be solved with algebra as motivation. Each volume contains a number of figures (67 in total), many applications, and a discussion of open problems (e.g. the convergence of Newton's method, finite projective planes, the inverse Galois problem).

From the Zentralblatt review: "The distinguishing features of the book are the following ones: 1) clearness, clarity and compactness of exposition; 2) the concentric style of presentation; 3) variety of skilfully selected examples (from very simple to very complex ones)."

[Note that the 1st edition was translated, but it is about a third as long and covers far less.]

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