Lectures on generalised cohomology -- On H-spaces and infinite loop spaces -- Functors between categories of vector spaces -- Natural vector bundles -- Several new concepts: Lucid and concordant functors, pre-limits, pre-completeness, the continuous and concordant completions of categories -- The categorical comprehension scheme -- Non-abelian sheaf cohomology by derived functors -- Foncteurs derives et K-theorie -- Relative functorial semantics: Adjointness results -- Minimal subalgebras for dynamic triples -- Categories of spectra and infinite loop spaces -- Homology of squares and factoring of diagrams.