Introduction
REVIEW OF CLASSICAL ALGEBRAIC KTHEORY AND REPRESENTAION THEORY
Notes on Notations
Category of Representations and Constructions of Grothendieck Groups and Rings
Category of representations and Gequivariant categories
Grothendieck group associated with a semigroup
K0 of symmetric monoidal categories
K0 of exact categories  definitions and examples
Exercises
Some Fundamental Results on K0 of Exact and Abelian Categories with Applications to Orders and Group Rings
Some fundamental results on K0 of exact and Abelian categories
Some finiteness results on K0 and G0 of orders and groupings
Class groups of Dedekind domains, orders, and group rings plus some applications
Decomposition of G0 (RG) (G Abelian group) and extensions to some nonAbelian groups
Exercises
K1, K2 of Orders and Group Rings
Definitions and basic properties
K1, SK1 of orders and grouprings; Whitehead torsion
The functor K2
Exercises
Some Exact Sequences; Negative KTheory
MayerVietoris sequences
Localization sequences
Exact sequence associated to an ideal of a ring
Negative Ktheory Kn, n positive integer
Lower Ktheory of group rings of virtually infinite cyclic groups
HIGHER ALGEBRAIC KTHEORY AND INTEGRAL REPRESENTATIONS
Higher Algebraic KTheoryDefinitions, Constructions, and
Relevant Examples
The plus construction and higher Ktheory of rings
Classifying spaces and higher Ktheory of exact categoriesconstructions and examples
Higher Ktheory of symmetric monoidal categoriesdefinitions and examples
Higher Ktheory of Waldhausen categoriesdefinitions and examples
Exercises
Some Fundamental Results and Exact Sequences in Higher KTheory
Some fundamental theorems
Localization
Fundamental theorem of higher Ktheory
Some exact sequences in the Ktheory of Waldhausen categories
Exact sequence associated to an ideal, excision, and MayerVietoris sequences
Exercises
Some Results on Higher KTheory of Orders, Group Rings and
Modules over "EI" Categories
Some finiteness results on Kn, Gn, SKn, SGn of orders and groupings
Ranks of Kn(?), Gn(?) of orders and group rings plus some consequences
Decomposition of Gn(RG) n = 0, G finite Abelian group;
Extensions to some nonAbelian groups, e.g., quaternion and dihedral groups
Higher dimensional class groups of orders and group rings
Higher Ktheory of group rings of virtually infinite cyclic groups
Higher Ktheory of modules over "EI" categories
Higher Ktheory of P(A)G, A maximal orders in division algebras, G finite group
Exercises
Modm and Profinite Higher KTheory of Exact Categories, Orders, and Groupings
Modm Ktheory of exact categories, rings and orders
Profinite Ktheory of exact categories, rings and orders
Profinite Ktheory of padic orders and semisimple algebras
Continuous Ktheory of padic orders
MACKEY FUNCTORS, EQUIVARIANT HIGHER ALGEBRAIC KTHEORY, AND EQUIVARIANT HOMOLOGY THEORIES
Exercises
Mackey, Green, and Burnside Functors
Mackey functors
Cohomology of Mackey functors
Green functors, modules, algebras, and induction theorems
Based category and the Burnside functor
Induction theorems for Mackey and Green functors
Defect basis of Mackey and Green functors
Defect basis for KG0 functors
Exercises
Equivariant Higher Algebraic KTheory Together with Relative
Generalizations for Finite Group Actions
Equivariant higher algebraic Ktheory
Relative equivariant higher algebraic Ktheory
Interpretation in terms of group rings
Some applications
Exercises
Equivariant Higher KTheory for Profinite Group Actions
Equivariant higher Ktheory (absolute and relative)
Cohomology of Mackey functors (for profinite groups)
Exercises
Equivariant Higher KTheory for Compact Lie Group Actions
Mackey and Green functors on the category A(G) of homogeneous spaces
An equivariant higher Ktheory for Gactions
Induction theory for equivariant higher Kfunctors
Exercise
Equivariant Higher KTheory for Waldhausen Categories
Equivariant Waldhausen categories
Equivariant higher Ktheory constructions for Waldhausen categories
Applications to complicial biWaldhausen categories
Applications to higher Ktheory of group rings
Exercise
Equivariant Homology Theories and Higher KTheory of Group Rings
Classifying space for families and equivariant homology theory
Assembly maps and isomorphism conjectures
FarrellJones conjecture for algebraic Ktheory
BaumConnes conjecture
DavisLück assembly map for BC conjecture and its identification with analytic assembly map
Exercise
Appendices
A: Some computations
B: Some open problems
References
Index
