(By Svante Janson, Tomasz Luczak and Andrzej Rucinski. Wiley, N.Y., 2000. ISBN: 0-471-17541-2.)

## 1    Preliminaries

1.1    Models of random graphs
1.2    Notes on notation and more
1.3    Monotonicity
1.4    Asymptotic equivalence
1.5    Thresholds
1.6    Sharp thresholds

## 2    Exponentially Small Probabilities

2.1    Independent summands
2.2    Binomial random subsets
2.3    Suen's inequality
2.4    Martingales
2.5    Talagrand's inequality
2.6    The upper tail

## 3    Small Subgraphs

3.1    The containment problem
3.2    Leading overlaps and the subgraph plot
3.3    Subgraph count at the threshold
3.4    The covering problem
3.5    Disjoint copies
3.6    Variations on the theme

## 4    Matchings

4.1    Perfect matchings
4.2    G-factors
4.3    Two open problems

## 5    The Phase Transition

5.1    The evolution of the random graph
5.2    The emergence of the giant component
5.3    The emergence of the giant: A closer look
5.4    The structure of the giant component
5.5    Near the critical period
5.6    Global properties and the symmetry rule
5.7    Dynamic properties

## 6    Asymptotic Distributions

6.1    The method of moments
6.2    Stein's method: The Poisson case
6.3    Stein's method: The normal case
6.4    Projections and decompositions
6.5    Further methods

## 7    The Chromatic Number

7.1    The stability number
7.2    The chromatic number: A greedy approach
7.3    The concentration of the chromatic number
7.4    The chromatic number of dense random graphs
7.5    The chromatic number of sparse random graphs
7.6    Vertex partition properties

## 8    Extremal and Ramsey Properties

8.1    Heuristics and results
8.2    Triangles: The first approach
8.3    The Szemerédi Regularity Lemma
8.4    A partition theorem for random graphs
8.5    Triangles: An approach with perspective

## 9    Random Regular Graphs

9.1    The configuration model
9.2    Small cycles
9.3    Hamilton cycles
9.4    Proofs
9.5    Contiguity of random regular graphs
9.6    A brief course in contiguity

## 10    Zero-One Laws

10.1    Preliminaries
10.2    Ehrenfeucht games and zero-one laws
10.3    Filling gaps
10.4    Sums of models
10.5    Separability and the speed of convergence

## Index

Svante Janson, svante.janson@math.uu.se.