**Summary:** This book is an extensive revision of the 2007 book * Random Graph Dynamics*. In contrast to RGD, the new version considers a small number of types of graphs, primarily the configuration model and inhomogeneous random graphs, but investigates a wide variety of dynamics. It describes results for the convergence to equilibrium for random walks on random graphs as well as topics that have emerged as mature research areas since the publication of the first edition, such as epidemics, the contact process, voter models, and coalescing random walk. Chapter 8 discusses a new challenging and largely uncharted direction: systems in which the graph and the states of their vertices coevolve.

At this point I have gotten over the fact that my book suffered a very late term abortion at Cambridge, and I have started going through the book correcting the useful comments made by the copyeditor, rewriting arguments to clarify them, and most important add putting punctuation in display, because otherwise the reader might keep going until they pass out. In addition I have added material to Chapters 1, 6, and 3 as indicated in the outline. The new plan is to clean up the current version and publish it early in 2025.

1.1. Branching Processes

1.2. Cluster growth as an epidemics

1.3. Cluster growth as a random walk

1.4. Long paths (rewritten)

1.5. CLT for the giant component

1.6. Combinatorial approach

1.7. Critical regime

1.8. Critical exponents (correction in 1.8.4 and other rewrites)

1.9. Threshold for connectivity

2.1. Configuration model

2.2. Limiting degree distribution approach

2.3. Subcritical cluster sizes

2.4. Distances between two randonly chosen vertices

2.5. First passage percolation

2.6. Critical regime

2.7. Percolation

3.1. Finitely many types

3.2. Motivating examples

3.3. Welcome to the machinge

3.4. Results for the survival probability

3.5. Survival probabilities for examples

3.6. Component sizes in the subcritical case

3.7. Multivariate Erdos-Renyi graphs (new 21 page section with an introguing open problem)

4.1. On the complete graph

4.2. Fixed infection times

4.3. General infection times

4.4. Miller-Volz equations

4.5. Rigorous derivations of the equations

4.6. Household model

4.7. Forest fires and epdiemics on Z^{2}

5.1. Basic Properties

5.2. Trees, random regular graphs

5.3. Power-law random graphs

5.4. Results for the star graph

5.5. Sub-exponential degree distributions

5.6. Exponential tails

5.7. Threshold-θ contact process

6.1. Basic definitions

6.2. Markov chains and electrical networks

6.3. Conductance

6.4. First degree distribution, min degree 3

6.5. Effect of degree 2 vertrices

6.6. Connected Erdos-Renyi graphs

6.7. Cutoff

6.8. Random regular graphs

6.9. Random walk on Galton-Watson trees (new material on biased walks)

6.10. Sparse Erdos-Renyi graphs

7.1. On Z^{d} and on graphs

7.2. In d=1 and in your colon

7.3. Coalescing random walk on the torus

7.4. Using ideas from Markov chains

7.5. Cooper's bound

7.6. Random regular graphs

7.7. Oliveira's results

7.8. Asymptotics for CRW densities

8.2. SIS epidemics

8.3. SIR epidemics

A.2. Azuma-Hoeffding inequality