You will find two sections below. Topic Pointers contains books recommended to me (by cited experts) regarding a particular subject or question. My shelf is a list of books that I own and either have (mostly) read or use as a reference.

Topic pointers

• Probability Measures on Metric Spaces, Parthasarathy — This book was recommends by Stroock, when I asked whether there exist convolutional roots of origin-symmetric unimodal distributions (like Gaussian, Cauchy or Levy)
• Probability Theory, Bauer — Introduction to measure-theoretic probability theory
• The Volume of Convex Bodies and Banach Space Geometry, Pisier (1989) — Self-contained treatment of fundamental results in convex geometry

My shelf

Probability and graphs

• Markov Chains, Norris
• Reversible Markov Chains and Random Walks on Graphs, Aldous
• The Probabilistic Method, Alon, Spencer
• Random Graphs, Janson, Luczak, Rucinski
• Random Graphs, Bollobas

Geometry, spectra, matrices and embeddings

• Lectures on Discrete Geometry, Matousek
• The Random Projection Method, Vempala
• Convex Bodies, Bonnesen, Fenchel
• Matrix Analysis, Horn, Johnson
• Topics in Matrix Analysis, Horn, Johnson
• Matrix Computations, Golub, van Loan
• Introduction to Circle Packing, Stephenson
• The Discrepancy Method, Chazelle

Algorithms and optimization

• Approximation Algorithms for NP-Hard Problems, Hochbaum
• Combinatorial Optimization, Cook, Cunningham, Pulleyblank, Schrijver
• Combinatorial Optimization: Polyhedra and Efficiency, Vol. A,B,C, Schrijver
• Combinatorial Optimization: Algorithms and Complexity, Papadimitriou, Steiglitz
• Integer and Combinatorial Optimization, Wosley
• Convex Analysis and Optimization, Bertsekas

Complexity, Information and Coding

• Elements of Information Theory, Cover, Thomas
• An Introduction to Computational Learning, Kearns, Vazirani
• An Introduction to Kolmogorov Complexity and Its Applications, Li, Vitànyi
• Quantum Computation and Quantum Information, Chuang, Nielsen
• Communication Complexity, Kushilevitz, Nisan

Groups and algebra

• Fuchsian Groups, Katok
• Representations and Characters of Groups, James, Liebeck
• The Theory of Group Characters and Matrix Representations of Groups, Littlewood
• Representation Theory: A First Course, Fulton, Harris
• Introduction to Commutative Algebra, Atiyah, MacDonald
• Linear Representations of Finite Groups, Serre

Combinatorics

• Circuits of the Mind, Valiant
• Additive Combinatorics, Tao
• Combinatorial Problems and Exercises, Lovasz
• Enumerative Combinatorics, Vols. 1 & 2, Stanley

Analysis

• Real Analysis, Royden
• Real and Complex Analysis, Rudin
• Functional Analysis, Rudin
• Functional Analysis, Lax
• Functional Analysis, Yoshida
• Complex Analysis, Ahlfors
• Conformal Mapping, Nehari
• Fourier Analysis on Groups, Rudin