**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.

- Despite assurances the copy editing would be light, the copyeditor did numerous rewrites of the test, including rewriting the preface.
- He evidently had some math training, but he made two dozen changes in the math which were wrong.
- One day he decided the names of examples should be in parentheses, but then on other days he forgot he made that change, etc etc.

At this point I have started going through the book correcting the roughly 100 useful comments made by the copyeditor, rewriting arguments to clarify them. In addition I am adding a half dozen new sections. Bowing to pressure to conform I am putting punctuation in displays. The new chapters will appear one at a time as they are finished. Sections that have been substantially changed are indicated.

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

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