Theory of Linear Operators in Hilbert Space
This classic textbook by two mathematicians from the USSR's prestigious Kharkov Mathematics Institute introduces linear operators in Hilbert space, and presents in detail the geometry of Hilbert space and the spectral theory of unitary and self-adjoint operators. It is directed to students at graduate and advanced undergraduate levels, but because of the exceptional clarity of its theoretical presentation and the inclusion of results obtained by Soviet mathematicians, it should prove invaluable for every mathematician and physicist. 1961, 1963 edition.
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I used the book for self-study on Hilbert Spaces, and it helped me a lot. The proofs are simple and sometimes pleasantly diverging from those found in standard textbooks.