Mathematics

Logic

• Kurt Gödel - Uber formal unentscheidbare Sätze der “Principia Mathematica” und verwandter Systeme I
• Kurt Gödel - On formally undecidable propositions of Principia Mathematica and related systems I
• Richard Zach - 'Uber formal unentscheidbare Sätze der Principia mathematica und verwandter Systeme I' (1931)
• Peter Smith - Gödel Without (Too Many) Tears
• Elliott Mendelson - Introduction to Mathematical Logic

Number Theory

• Richard Dedekind - Was sind und was sollen die Zahlen?
• David E. Joyce - Notes on Richard Dedekind's Was sind und was sollen die Zahlen?

Algebra

• Joseph J. Rotman - An Introduction to the Theory of Groups 4th ed 1995 GTM148
• Homer Betchell - The Theory of Groups 1971
• Thomas Britz, Peter Cameron - Partially Ordered Sets
• Gerge Grätzer - Lattice theory Foundation

Universal Algebra

• G.M. Bergman - An Invitation to General Algebra and Universal Constructions (Web Draft, 1998)
• G.M. Bergman - An Invitation to General Algebra and Universal Constructions 3.0
• G.M. Bergman - Some Category-Theoretic Ideas in Algebra
• G.M. Bergman - Colimits of Representable Algebra-valued Functors
• Martin Hyland - The Category Theoretic Understanding of Universal Algebra Lawvere Theories and Monads
• J. Adler, J. Schmid, M. Sprenger - Model Theory, Universal Algebra and Order
• J. Adámek, J. Rosický, E.M. Vitale - Algebraic Theories A Categorical Introduction to General Algebra (2008)
• J. Adámek, J. Rosický, E.M. Vitale - Algebraic Theories A Categorical Introduction to General Algebra (2009)
• P. Freyd - Algebra Valued Functors in General and Tensor Products in Particular
• F. William Lawvere - Functorial Semantics of Algebraic Theories
• S. Burris, H.P. Sankappanavar - A Course in Universal Algebra
• S. Burris, H.P. Sankappanavar - A Course in Universal Algebra (2012)

Linear Algebra

• E.H. Connell - Elements of Abstract and Linear Algebra
• Jim Hefferon - Linear Algebra

Complex Analysis

• Lars V. Ahlfors - Complex Analysis 2ed McGraw Hill 1966
• Walter Rudin - Real and Complex Analysis McGraw Hill 1970
• Walter Rudin - Principles of Mathematical Analysis 3ed McGraw Hill 1976

Real Analysis

• Tom M. Apostol - Calculus Vol 1: One Variable Calculus and Linear Algebra 2ed Wiley 1967 (djvu)
• Tom M. Apostol - Calculus Vol 2: Multi Variable Calculus and Linear Algebra 2ed Wiley 1969 (djvu)
• Tom M. Apostol - Calculus Vol 1: One Variable Calculus and Linear Algebra 2ed Wiley 1967 (pdf)
• Tom M. Apostol - Calculus Vol 2: Multi Variable Calculus and Linear Algebra 2ed Wiley 1969 (pdf)
• Michael Spivak - Calculus on Manifolds Addison Wesley 1965
• Teodora-Liliana T. Radulescu, Vicentiu D. Radulescu, Titu Andreescu - Problems in Real Analysis Advanced Calculus on the Real Axis

Category Theory

• Michael Barr, Charles Wells - Category Theory for Computing Science

Geometry

• Manfredo Do Carmo - Riemannian Geometry Birkhauser 1992

Algebraic Topology

• Allen Hatcher - Algebraic Topology

Algebraic Geometry

• J.S. Milne - Algebraic Geometry

Various

• Douglas Stinson - Cryptography: Theory and Practice
• Fibonacci Numbers and The Golden Section
• Arthur Benjamin and Michael Shermer - Secrets of Mental Math
• Wendy Lichtman - Secrets, Lies, and Algebra
• G.A. MIller - A Few Classic Unknowns in Mathematics
• Abramowitz, Stegun - Handbook of Mathematical Functions
• Math Calculus Bible
• Encyclopedic Dictionary of Math (AN)
• Encyclopedic Dictionary of Math (OZ)