The aim of this monograph is to describe the main concepts and recent advancesin multiscale finite element methods. This monograph is intended forthe broader audience including engineers, applied scientists, and for those whoare interested in multiscale simulations. The book is intended for graduatestudents in applied mathematics and those interested in multiscale computations.It combines a practical introduction, numerical results, and analysis ofmultiscale finite element methods. Due to the page limitation, the materialhas been condensed.