Textbook for Bayesian econometrics I am looking for a theoretically rigorous textbook on Bayesian econometrics, assuming a solid understanding of frequentist econometrics.
I would like to suggest one work per answer, so that recommendations can be voted up or down individually.
 A: Bayesian Econometrics, by Gary Koop (2003) is a modern rigorous coverage of the field that I recommend. It is in addition completed by a book of exercises: Bayesian Econometric Methods (Econometrics Exercises) by Gary Koop, Dale J. Poirier and Justin L. Tobias (2007). 
A: I suggest "Bayesian Data Analysis" by Gelman et al.: 
Gelman, A., Carlin, J., Stern, H., Dunson, D., Vehtari, A., Rubin, D. (2013). Bayesian Data Analysis, Third Edition. New York: Chapman and Hall/CRC.
A: An Introduction to Bayesian Inference in Econometrics
by Arnold Zellner (1971)
From the cover:

"This is the first book in econometrics to look at models and problems
  from the Bayesian point of view. [M]any comparisons of Bayesian and
  non-Bayesian results are presented. [...] An Introduction to Bayesian
  Inference in Econometrics will be of value as a guide to Bayesian
  Econometrics for graduate-level students and as a reference volume for
  researchers."

A: While it's made for marketing, I'd suggest Bayesian Statistics and Marketing by Rossi, Allenby & McCulloch for Bayesian inference in economic models.
A: I might consider Contemporary Bayesian Econometrics and Statistics by John Geweke. It is relatively brief. The first three chapters cover the sort of foundational stuff you find in any Bayesian analysis book. The next chapter is the linear model with a tad of non-linear regression, followed by latent variables and missing data, then time-series and closed with model comparison and evaluation. There's not very much on panel data or semi/nonparametric estimation.
