The following books have been suggested as potential projects:

Invitation to Ergodic Theory – Silva

Geometry and Billiards – Tabachnikov

Groups Graphs and Trees – Meier

Elliptic curves, Modular Forms, and their Lfunctions – LozanoRobledo

Contributions to the Founding Theory of Transfinite Numbers – Cantor

Categories for the working mathematician – Mac Lane

Heads or Tails: An Introduction to Limit Theorems in Probability – Lesigne

Complex Algebraic Curves – Kirwan

Fractal Geometry – Falconer

Metric Spaces, Convexity, and Nonpositive Curvature – Papadopoulous

A First Course in Dynamics – Hasselblatt and Katok

Set Theory and Metric Spaces – Kaplansky

Mostly Surfaces – SchwartzMany other topics are possible, like voting theory, logic, etc.