Several important aspects of moduli spaces and irreducible holomorphic symplectic manifolds were highlighted at the conference Algebraic and Complex Geometry held September 2012 in Hannover, Germany. These two subjects of recent ongoing progress belong to the most spectacular developments in Algebraic and Complex Geometry. Irreducible symplectic manifolds are of interest to algebraic and differential geometers alike, behaving similar to K3 surfaces and abelian varieties in certain ways, but being by far less well-understood. Moduli spaces, on the other hand, have been a rich source of open questions and discoveries for decades and still continue to be a hot topic in itself as well as with its interplay with neighbouring fields such as arithmetic geometry and string theory. Beyond the above focal topics this volume reflects the broad diversity of lectures at the conference and comprises 11 papers on current research from different areas of algebraic and complex geometry sorted in alphabetic order by the first author. It also includes a full list of speakers with all titles and abstracts.

Preface.- Introduction.-A. Frühbis-Krüger, R. Kloosterman, M. Schütt: Introduction.-M.A. Barja, L. Stoppino: Stability conditions and positivity of invariants of fibrations.-A. Beauville: On the second lower quotient of the fundamental group.-M. Blume: McKay correspondence over non algebraically closed fields.-L. Caporaso: Gonality of algebraic curves and graphs.-F. Catanese: Caustics of plane curves, their birationality and matrix projections.-O. Fujino, Y. Gongyo: On images of weak Fano manifolds II.-N. Hitchin: The hyperholomorphic line bundle.-H. Hollborn, S. Müller-Stach: Hodge numbers for the cohomology of Calabi-Yau type local systems.-E. Markman: Lagrangian fibrations of holomorphic-symplectic varieties of K3^[n]-type.-T. Peternell, F. Schrack: Contact Kähler Manifolds: Symmetries and Deformations.- Complete List of talks.- List of participants.