The undergraduate course
The undergraduate course, called the Mathematical Tripos, is a threeyear or a fouryear course. If you graduate after three years, you receive the BA degree. If you graduate after four years, you receive the BA and MMath degrees. In both cases, you automatically qualify, after a further three years, for the MA degree. In order to stay for the fourth year, you have to achieve a high standard in the third year.
It is widely considered to be a very tough course; and correspondingly rewarding. The range of subjects offered is exceptionally wide: you can learn about everything from black holes to the most abstruse problems in logic.
Two features of the course are unusual.
First, Mathematics cannot be taken jointly with any other course (no joint honours, no MathswithFrench)  it is a course for those wishing to specialise in Mathematics. There is no possibility of taking papers from other subjects, except in the first year when you can choose to take the Physics paper from the Natural Sciences Tripos in place of 25% of the Mathematics course.
Second, the examinations are nonmodular in structure: it is not the case that each examination paper is devoted to an individual lecture course, Instead, there are four threehour papers at the end of each year. In the first year, two topics are examined on each paper and in the second and third years each paper is crosssectional, meaning that questions on the individual lectures courses are spread over the four papers. This allows you the flexibility to choose how many courses you wish to revise for the examination and therefore to work at your own pace, which is important in mathematics.
The following documentation is available:

Information about admissions in mathematics, including notes for Scottish candidates, details of the STEP examination and a reading list.

Information about the mathematics course, including options, general descriptions of the lecture courses and detailed syllabuses.

A study skills guide and and a guide for supervisors.
The angle of the wake of a body moving steadily in deep water is always 2arcsin(1/3). Not very many people know that, but it is one of the many fascinating results proved in the Mathematical Tripos.