[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.]