Book References [honours maths in UK]

[ShakilasSalafi]

Hello I am doing an honours course in Maths in India. I am in my second year. We mostly read books written by Indian authors and some US authors. However, I would like to know what books undergraduates in the UK refer to for the following topics, (since I wish to do my Masters and my Doctorate in the UK) :

1. Abstarct Algebra
2. Real Analysis
3. Complex Analysis
4. Analytical Mechanics*
5. General Topology

I feel knowing the books referred by the students in the UK will help in my preparations to get in any university ther.
*In India there two different courses in Mechanics, one which is more abstract is for Maths students and the other one which is more "physical" is for physics students.

 

[IDValour]

There's usually a fair degree of overlap between texts used in the UK and texts used in the US, although it quite naturally varies by University and Professor. Having said that if you're interested in becoming acquainted with the mechanics of a UK mathematics degree then you should hopefully be able to profit from the Cambridge University lecture notes (some of which include suggestions for supplementary/further reading) which have been posted online at this address: http://www.maths.cam.ac.uk/studentreps/tripos.html
A small number of these are restricted to students of the University itself, but most are free for you to access.

Edit:

Just realized it may not be clear what the correspondence for each part is, so here's a quick list:
Part IA = First Year
Part IB = Second Year
Part II = Third Year
These 3 parts make up a Bachelor's qualification in Mathematics from Cambridge.
Part III is somewhat separate from this and constituents a Master's degree in Mathematics, or Master of Advanced Study if taken by students outside of Cambridge. It has a reputation for being one of the best and most gruelling maths courses available in the world.