Conceptual overview: Self-information, Mutual information, uncertainty, entropy
Trying to answer the question myself, with my textbook at hand. So far, I am here:


Self-information of an event: uncertainty of an event.
$$I(x_i) = \log \frac{1}{P(x_i)} = -\log P(x_i)$$
Self information of a vector event:
$$I(x_i y_i) = -\log P(x_i,~y_i)$$
Mutual information between two events: the information one event (experiment outcome) gives us about the other event:
$$I(x_i;y_i) = \log \frac{P(x_i,~y_i)}{P(x_i) P(y_i)}$$
$$I(x_i y_i) = I(x_i) + I(y_i) - I(x_i; y_i)$$
Uncertainty: the formula of it is the same as self-information of an event. So I'll assume they are the same.
Average mutual information: The information one gives about the other when observer the former. Clumsy notation: 
$$I(X; Y) = E[I(x_i; y_i)]$$
Entropy: the average amount of information that is revealed by observing an event. (I know the relationship to Huffman coding here.) Clumsy notation:
$$H(X) = E[I(x_i)]$$
Conditional entropy: the amount of information (about $X$) that is left to be discovered after observing the given ($Y$).
$$H(X|Y) = H(X) - I(Y;Y)$$


\begin{align}
I(X; Y) &amp;= H(X) - H(X | Y) \\
\text{mutual} &amp;= \text{a priori} - \text{a posteriori}
\end{align}


Conditional self-information: the information that is contained within the outcome of a certain event ($x_i$), after already knowing the outcome of another event ($y_i$).
$$I(x_i | y_i) = -\log P(x_i | y_i)$$
Relations:
$$I(x_i | y_i) = I(x_i) - I(x_i; y_i)$$
\begin{align}
I(x_i; y_i) &amp;= I(x_i) - I(x_i | y_i) \\
\text{mutual} &amp;= \text{a priori} - \text{a posteriori}
\end{align}