This series of 4 talks will be a minicourse on Banach spaces
of continuous functions which have few operators, projections,
injections etc. In particular they can be indecomposable and
nonisomorphic with their hyperplanes. To obtain this linear operator
level rigidity one needs to construct compact Ks which are not only
rigid in the usual sense, i.e., in terms of continuous mappings on K.
One needs to deal with weak* continuous functions from K into the space
M(K) of Radon measures on K, so the combinatorics of the constructions
needs stronger conditions than for endo-rigid Boolean algebras or
strongly rigid compact spaces. We will present main arguments leading to
C(K)s with the required properties but the proofs of many lemmas will be
omitted. The talks should be accessible to everyone with general
analytic and topological background.