Modern macroeconomic theory is the study of dynamic general equilibrium economic models. Models are defined broadly and allow for situations where markets do not always clear and where prices do not necessarily adjust instantaneously. This text provides an introduction to the study of such models: time can either be modelled in a discrete or continuous fashion, and the environment may be either deterministic or stochastic -- this generality accommodates both business cycle and economic growth modelling.The purpose of the book is to teach first the tools employed in modern macroeconomic theory and second the topics most often encountered in macroeconomic debate. While the focus of the textbook is on macroeconomic modelling, the tools that are employed can also be applied to other fields in economics; for example, natural resource and environmental economics and industrial organization. Throughout the text the reader is exposed to both methodology and applications -- the scope and reach of a reader's own modelling is of course entirely a function of her own ingenuity with economic questions of interest.