<p>Freely available math-olympiad training handouts by MIT Professor Yufei Zhao, collected from his teaching at national and international training programmes – including the Canadian IMO Training Camps, the US Math Olympiad Program (MOP), AwesomeMath, and UK Trinity Training. The material targets students already working at senior olympiad level.</p><ul><li>Algebra: integer polynomials, inequalities, advanced polynomial techniques, and linear-algebra tricks.</li><li>Combinatorics: bijections, counting in two ways, tiling, algebraic techniques, and generating functions.</li><li>Geometry: cyclic quadrilaterals, three core lemmas, power of a point, spiral similarity, and projective tools.</li><li>Number theory: modular arithmetic; Fermat, Euler and Wilson; and working with a^n ± 1.</li><li>Recommended starting points: "Cyclic Quadrilaterals – The Big Picture" and "Three Lemmas in Geometry".</li><li>A separate book-recommendation list covers introductory through advanced olympiad preparation.</li></ul>