This volume contains four papers written by participants of the international conference on Higher Dimensional Algebraic Varieties held at the Research Institute of Mathematical Sciences (RIMS) at Kyoto University (Japan). Rather than an ordinary proceedings of the conference, the editors have compiled a selection of independent, full expositions on topics of fundamental importance in algebraic geometry: moduli spaces of abelian surfaces, rational curves on algebraic varieties, 3-dimensional flips, and the theory of elliptic fibrations. The authors - including a Fields medalist and the founder of fundamental results in algebraic geometry - discuss the topics fully, giving complete proofs of new results, technical preparations, and an historical overview. The book is suitable for graduate students and research mathematicians interested in algebraic geometry.