1 Introduction and Background.- 2 Rational and Other Explicit Strong Solutions.- 3 Weak Solutions and Related Topics.- 4 Geometric Properties.- 5 Capacities and Isoperimetric Inequalities.- 6 Laplacian Growth and Random Matrix Theory.- 7 Integrability and Moments.- 8 Shape Evolution and Integrability.- 9 Stochastic Löwner and Löwner-Kufarev Evolution.- References.- List of Symbols.- Index.