LC call numbers divide books into classes, subclasses, topics, and subtopics.
For example, Fermat's enigma : the epic quest to solve the world's greatest mathematical problem by Simon Singh has the call number: QA244 .S55 1997.
On the book spine, the call number would appear like this:
QA
244
.S55
1997
QA 
is the class and subclass. Q is Science and QA is Mathematics.
 Read the first line in alphabetical order: When there are two letters, Q comes before QA, which comes before QC, etc.

244 
is the classification number for the subject. 244 is Higher congruences, residues. Fermat's Theorem.
 Read the second line as a whole number: 80 comes before 793, for example.

.S55 
is a combination of letters and numbers that usually represents the author or publisher's name.
It may also represent a more narrow topic or the author. In this case, .S55 represents the author, Simon Singh.
 Read the letter alphabetically but read the number as a decimal. So .P43 comes after .P422

1997 
is the year of publication, and identifies separate editions of a text.
 Read in chronological order.
