| Week | Dates | Subjects | References | Exercises | More |
| 1 | 11.1 12.1 | Linear and normed spaces. Zorns Lemma. Existence of a Hamel basis. Semi norms and quotient spaces. | 2-17, 50-67, 210-213. | Exercise-1 | Selected solutions-1 |
| 2 | 18.1 19.1 | Basic topology. Banach spaces. Completion theorem. | 17-48, 67-72. | Exercise-2 | Basic definitions in topologySelected solutions-2 |
| 3 | 25.1 26.1 | Category theorem. Bounded linear operators. The spaces B(X,Y). Open mapping theorem (part 1). | 246-249, 82-103, 117-119, 285-287. | Exercise-3 | Selected solutions-3 |
| 4 | 1.2 2.2 | Open mapping theorem (part 2). Closed operators. Closed graph theorem. Uniform boundedness theorem. | 285-297, 249-255 | Exercise-4 | None |
| 5 | 8.2 9.2 | Linear functionals. The dual space. Hahn Banach theorem (part 1) | 103-111, 120-125, 213-218 | Exercise-5 | None |
| 6 | 15.2 16.2 | Hahn Banach theorem (part 2). Reflexive spaces. | 218-224, 239-246 | Exercise-6 | None |
| 7 | 22.2 23.2 | The dual operator. Systems in separable Banach spaces. | 231-239 | Exercise-7 | None |