The Metropolis Algorithm 
I Know how to apply the Metropolis Algorithm, but I'd be grateful if someone could explain to me the reasoning behind the steps in the algorithm. I've tried in vain looking for the original paper.
Thanks.

The idea of the algorithm, is using one distribution (the transition distribution) in order to sample a different one (the original distribution). The assumption is that the original distribution is calculable, but that it is too difficult to sample directly. Ideally, the transition distribution should be "close enough" to the original distribution.
In order to do that, we have to sample in such a way where we don't follow the transition distribution "blindly", but rather use the original distribution to weigh how likely it is to actually sample the next value, rather than the old one.
It can be shown, (by simple summation of the probabilities) that the stationary distribution of the process - if there is one (if I'm not mistaken, in order for there to be one, the transition distribution has to satisfy some conditions that would ensure the sampling is "close enough" to the original distribution) - is indeed the distribution of the original distribution.
A common case which uses this algorithm, is the Gibbs sampling algorithm - on large graphical models. The transition distribution used is a single variable value change.
