In this talk, we introduce the Markov lemma and discuss its 
application to the multiterminal source coding problems.First, we 
briefly review the Shannon's first coding theorem & the rate 
distortion theory,  and explain the intuition behind them using the 
concepts of typical sequences. Then we introduce the Markov Lemma, an 
important tool for us to perform extensions not only to noiseless 
source coding problems for multiterminal configurations but also to 
rate-distortion problems for such configurations. After that, several 
concrete multiterminal source coding problems are explained to show 
how to use the Markov Lemma for them. The problems we discuss include 
the Slepian-Wolf problem, the source coding with side information, the 
rate distortion with side information and the rate distortion for a 
more general case.