Dimension theory This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds and on the concepts of global analysis and geometry such as jet prolongations of manifolds mappings and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry global analysis differential equations on manifolds and mathematical physics and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field