It all falls under the general heading of music theory, but more precisely it’s considered "tonal harmony." (Which includes modulation.)
This is typically covered in a music major’s basic 4 semester core theory sequence, often spread out like this:
First semester - Rudiments, major and minor scales, triads, basic part writing, cadences
Second semester - part writing using dominant and predominant chords, including V7, IV, viio, ii, vi, and iii.
Third semester - applied/secondary dominants and tonicization, borrowed chords, possibly modulation
Fourth semester - other predominant harmonies including augmented sixth chords and the Neopolitan; often the fourth semester also contains an introduction to 20th century practices, including the use of modes, pitch class set analysis, etc...
Also, the trend these days is to also spend some time on Neo-Riemannian approaches to theory (which involves the functional tendencies of tones within a texture.)
Music theory is an enormous discipline that has many facets. It’s somewhat similar to mathematics:
Rudiments - Arithmetic
Tonal Harmony - Algebra
Transformational Theory - Number Theory
Jazz Harmony - Calculus
Schenkerian Analysis - Differential Equations
Atonal Systems - Set theory and fractal geometry
...plus a few hundred more esoteric things. There are things that everybody knows and things that maybe only 4 people in the world understand.
For fun, you guys should check out the online journal for the Society of Music Theory:
http://societymusictheory.org:16080/mto/
Browse through the back issues. You’ll be amazed at how rich, varied, and often incomprehensible the stuff is!
http://www.schenkerguide.com/
http://jan.ucc.nau.edu/~tas3/bachindex.html
http://www.pianoworld.com/ubb/cgi-bin/ultimatebb.cgi?/topic/2/6873.html
A quick note on Schenker (and some others):
Schenker’s analysis technique is detailed in his third major book "Der Freie Satz" (Free Composition). It was intended to be studied after the student was well versed in the material of his first two books, "Counterpoint" and "Harmony."
Also interesting is that several major theorists also had the same general idea, publishing books on Counterpoint and Harmony - in that order.
Modern theory pedagogy seems to take a different approach - most people study a combination of the two at first (Harmony and Voice Leading) and move on to Counterpoint later. Regardless, everyone’s in agreement that a student of Schenkerian analysis should already be well-versed in counterpoint and harmony.
The path of study I might suggest would be to pick up a good undergraduate theory text (Aldwell/Schacter, Kostka/Payne, etc...) and do a LOT of writing. Music theory is both information and skill, and doing a lot of written exercises and analysis can be very helpful.
