Chance and necessity in evolution is a fundamental theme of biology. How can we understand this dynamics starting from its molecular basis, which lies in genes and their interactions? How do adaptation and functional innovation take place in the sea of stochastic changes of molecular evolution? What can we learn about this process from genomic data and from evolution experiments, for example in bacterial systems? Such questions are addressed by modern evolutionary genetics. This course provides an introduction suitable for physicists to this rapidly developing field of science.

1. Basic concepts and evolutionary forces (week 1, ML)
Populations, genotypes, phenotypes, mutations, fitness, reproductive fluctuations, DNA, RNA, proteins, recombination, diploids and haploids.

2. Evolution of regulation (week 2, ML)
Transcriptional processes, evolution of regulatory DNA, genomics and inference of selection.

3. Evolution of a complex phenotype: RNA structures (week 3, ML)
RNA secondary and tertiary structure, sequence-phenotype map, fitness and modularity of RNA processing.

4. Theory of fitness landscapes (weeks 4 and 5, JK)
Geometry of sequence space; random ensembles of fitness landscapes, sign epistasis, measures of landscape ruggedness, explicit genotype-phenotype maps (RNA, proteins).

5. Fitness landscapes in bacterial evolution (week 6, JK)
Empirical fitness landscapes, recombination spaces.

6. Evolution of the influenza virus (week 7, ML)
sequence evolution, antigenic evolution, red queen dynamics.

7. Deterministic mutation-selection models (weeks 8, 9, JK)
"Quasispecies" dynamics in discrete and continuous time, linearization. Mutation-selection balance as an eigenvalue problem, exactly solvable cases, asymptotic results: maximum principle, quantum-mechanical approach. Epistasis and robustness, nonlinear models: diploids and recombination.

8. Clonal interference (week 10, JK)

9. Evolution under time-dependent selection (weeks 11 and 12, ML)