A subject that escapes mention in the / book is how to control the size of large delimiters if the automatic sizing done by left and right produces unsatisfactory results. The automatic sizing has two limitations: First, it is applied mechanically to produce delimiters large enough to encompass the largest contained item, and second, the range of sizes is not even approximately continuous but has fairly large quantum jumps. This means that a math fragment that is infinitesimally too large for a given delimiter size will get the next larger size, a jump of 3pt or so in normal-sized text. There are two or three situations where the delimiter size is commonly adjusted, using a set of commands that have `big' in their names.
The first kind of situation is a cumulative operator with limits above and below. With left and right the delimiters usually turn out larger than necessary, and using the |Big| or |bigg| sizes instead gives better results:
\biggl[\sum_i a_i\Bigl\lvert\sum_j x_{ij}\Bigr\rvert^p\biggr]^{1/p}
The second kind of situation is clustered pairs of delimiters where
left and right make them all the same size (because that is
adequate to cover the encompassed material) but what you really want
is to make some of the delimiters slightly larger to make the nesting
easier to see.
\left((a_1 b_1) - (a_2 b_2)\right)
\left((a_2 b_1) + (a_1 b_2)\right)
\quad\text{versus}\quad
\bigl((a_1 b_1) - (a_2 b_2)\bigr)
\bigl((a_2 b_1) + (a_1 b_2)\bigr)
The third kind of situation is a slightly oversize object in running
text, such as 
where the
delimiters produced by left and right cause too much line
spreading. In that case bigl and bigr can be used to produce
delimiters that are slightly larger than the base size but still able to
fit within the normal line spacing:
.
In ordinary / big, bigg, Big, and Bigg delimiters aren't scaled properly over the full range of / font sizes. With the amsmath package they are.