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 L-functions – Lozano-Robledo
• 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 – Schwartz
  Many other topics are possible, like voting theory, logic, etc.