chapter 1 Introduction -- chapter 2 A rst look at zeta functions and heat traces -- chapter 3 Zeta functions on generalized cones and related manifolds -- chapter 4 Calculation of heat kernel coeÆcients via special cases -- chapter 5 Heat content asymptotics -- chapter 6 Functional determinants -- chapter 7 Casimir energies -- chapter 8 Ground-state energies under the inuence of external fields -- chapter 9 Bose-Einstein condensation of ideal Bose gases under external conditions -- chapter 10 10Conclusions.