1. Metric spaces.- 2. Linear spaces and normed spaces.- 3. Continuous linear operators in Banach spaces.- 4. Weak topologies.- 5. Optimization and observability of linear systems.- 6. Systems governed by ordinary differential equations.- 7. Systems with distributed parameters.- 8. Differential and integral equations in Banach spaces.- Appendix. Necessary and sufficient condition for weak duality.- Author index.- List of symbols.