The Library of Congress Classification System is an alpha-numeric system in which major categories correspond to bodies of knowledge.

It was developed by Herbert Putnam in 1897, and was designed to meet the needs of the Library of Congress's huge collection of books.

“Most major library classification schemes have their origins in the nineteenth century and reflect either (1) an ideology that thought it possible to embrace the whole world of knowledge or (2) a pragmatic attempt to group similar documents together on the shelves of a major library…The ‘world of knowledge’ is divided into suitable classes and new subject concepts may be added to each when necessary. These schemes are referred to as enumerative schemes. Seriously dated in their fundamental conceptual approach to knowledge, they survive, as libraries can still make them work effectively for shelf arrangement.”
-John Feather and Paul Sturges, eds. International Encyclopedia of Information and Library Science . New York: Routledge, 1997. “Classification,” pp. 57-58.
 
The LC Classification System organizes all knowledge into "classes" such as Science, Art, Literature, etc. These classes are assigned alpha-numeric call numbers that make it easy to organize and find library materials (like books). There is a flow through general areas of knowledge. (A) is general knowledge, then we have philosophy & religion (B), then history, then economic activity. (R) flows from (Q), so does (S) & (T). (Z) is bibliography.

LC Classification breaks down each discipline into more specific areas. For example, materials under the classification of Art are assigned call numbers beginning with the letter "N." More specific areas are assigned more specific numbers - NA, Architecture; NA200, Architecture/History/General Works; NA208.5, Architecture/History/Grotesque in Architecture. These numbers can get very specific. For example, NA1019.5 .N45 relates to late neoclassicism in 19th Century Hungarian architecture. (As I said, this system attempts to classify ALL knowledge.)

Let's look at a Library of Congress call number in more detail:

E 183.8 .M6 H54 1974