You should really already have a copy of this, but I include it anyway because it is an incredible book. Has some use for the Numbers and sets first year course.

Transition book from pre-university mathematics; covers half of first year group theory (Orbit stabilizer and isomorphism theorem), spherical/hyperbolic geometry, elementary results in quadratic forms

After 45 years this is still the best first year analysis book on the market, with more stimulating problems that Rudin. Also written in a "transition to university maths" style.

Covers the material for the latter half of the rings and modules optional first year course (which you should take!)

First year mechanics book. Perhaps a bit lacking in tripos-difficulty and length problems...

Straightforwardly readable coverage of second and part of third year quantum mechanics.

Many interesting problems and coverage of Analysis II and an alternative view of elementary complex analysis.

Covers the latter half of the second year geometry course. Provides quality solutions to exercises if you are having difficulty.

Despite its size it only covers the first half of the course using slightly annoying conventions. Provides extensive experience with finite groups (up to order 1000 in fact!)

Covers more elementary topics in the Riemann surfaces course. Absolute classic book .

Slow paced and readable introduction to Galois theory. Covers most of the third year course.

2nd year Markov chains and more!

Comprehensive coverage of Algebra for the first two years, but a bit light on Representation and Galois theory.