Drop me (mylastname at imperial.ac.uk) a line if something here is broken or missing.
Sheet 1
and solutions.
Sheet 2
and solutions.
Sheet 3
and solutions.
Sheet 4
and solutions.
Sheet 5
and solutions.
Sheet 6
and solutions.
Sheet 7
and solutions.
Sheet 8
and solutions.
Sheet 9
and solutions.
J.B. Fraleigh, A First Course in Abstract Algebra, Addison Wesley
R.. Allenby, Rings, Fields and Groups, Arnold
W. Ledermann, Introduction to Group Theory
I.N. Herstein, Topics in Algebra
For the linear algebra part, you might like to try
S. Lang, Linear Algebra
J. Fraleigh and R. Beauregard, Linear Algebra, Addison Wesley
S. Lipschutz and M. Lipson, Linear Algebra, Schaum Outline Series, McGraw Hill
Some lectures, for various reasons, were not recorded on Panopto. Here are links to scanned lecture notes for Lecture 1, Lecture 2, Lecture 7, Lecture 13, and Lecture 28.