For Logic
Book Of Proof by Richard Hammack (For Basic Proof-writing)
How to Prove It by Daniel J. Valleman (For Good Proof-writing)
For Set Theory
Classic Set Theory: For Guided Independent Study by D. C. Goldrei (for Axiomatic treatment)
For Abstract Algebra
A book of Abstract Algebra by Pinter (Good if you want to see algebraic structure in surroundings)
On Indian Scientists and Mathematicians
Indian
Mathematics
Engaging with the World
from Ancient to Modern Times by George Gheverghese Joseph (I can't attach the PDF link, but it is available, you just need to find it patiently)