This monograph presents recent developments in quantum field theory at finite temperature. By using Lie groups, ideas from thermal theory are considered with concepts of symmetry, allowing for applications not only to quantum field theory but also to transport theory, quantum optics and statistical mechanics. This includes an analysis of geometrical and topological aspects of spatially confined systems with applications to the Casimir effect, superconductivity and phase transitions. Finally, some developments in open systems are also considered. The book provides a unified picture of the fundamental aspects in thermal quantum field theory and their applications, and is important to the field as a result, since it combines several diverse ideas that lead to a better understanding of different areas of physics.Contents:General Principles:Elements of ThermodynamicsElements of Statistical MechanicsPartition Function and Path IntegralZero Temperature Interacting FieldsThermal Fields:Thermofield Dynamics: Kinematical Symmetry Algebraic BasisThermal Oscillators: Bosons and FermionsThermal Poincaré and Galilei GroupsThermal PropagatorScattering Process at Finite TemperatureTopics on Renormalization TheoryWard-Takahashi Relations and Gauge SymmetryApplications to Quantum Optics:Thermalized States of a Field ModeNonclassical Properties of Thermal Quantum StatesSU(2) and SU(1,1) Systems: EntanglementCompactified Fields:Compactified FieldsCasimir Effect for the Electromagnetic FieldCasimir Effect for FermionsCompactified λφ4 TheoryPhase Transitions in Confined Systems: Application to Superconducting FilmsSecond-Order Phase Transition in Wires and GrainsFirst-Order Phase Transitions in Confined SystemsApplications to Open Systems:Thermo-Algebras in Phase Space: Quantum and Classical SystemsReal-Time Method for Nonequilibrium Quantum MechanicsDressed and Bare State Approaches to the Thermalization ProcessReadership: Academics, students and researchers in diverse areas such as particle physics, quantum optics, condensed matter theory, transport theory and quantum mechanics in phase space; applied mathematicians interested in using methods of mathematics to physical systems.