Logic:

--mathematical

Enderton, "A mathematical introduction to logic" then Shoenfield's classic "Mathematical logic"

Cori and Lascar, "Mathematical logic: a course with exercise" for exercises for self-study

Manin, "A course in mathematical logic" for additional enrichment

--computational

Van Dalen's "Logic and Structure" and then Fitting, "First Order Logic and Automated theorem proving" to fill in the gaps

--philosophical

From Frege to Goedel: a sourcebook in mathematical logic

additional works by Frege and Cantor in dover reprints or in the original.

"Goedel's Proof" by Nagel

"Goedel, Escher and Bach" by Hofstadter

--modal and fuzzy

Goldblatt, "Logics of Time and Computation" (Introduction to modal logic through temporal logic)

Bergmann, "An introduction to many valued and fuzzy logic"

Calculus:

Apostol, "Calculus" 2 volumes (Still a classic)

Demidovich, "Problems in mathematical analysis" (Classic drill book)

Topology:

Viro, "Elementary Topology Problem Textbook" (Based on a classic course)

Modern Abstract Algebra:

Jacobson, "Basic Algebra" volumes 1 and 2

History of Western Philosophy:

Basic primary sources in western philosophy (Not a textbook!)