  This book introduces a new context for global homotopy theory, i.e.,
equivariant homotopy theory with universal symmetries. Many important
equivariant theories naturally exist not just for a particular group, but in a
uniform way for all groups in a specific class. Prominent examples are
equivariant stable homotopy, equivariant $K$-theory or equivariant bordism.
Global equivariant homotopy theory studies such uniform phenomena, i.e., the
adjective `global' refers to simultaneous and compatible actions of all compact
Lie groups.
  We give a self-contained treatment of unstable and stable global homotopy
theory, modeled by orthogonal spaces respectively orthogonal spectra under
global equivalences. Specific topics include the global stable homotopy
category, operations on equivariant homotopy groups, global model structures,
and ultra-commutative multiplications. The book includes many explicit examples
and detailed calculations.
