Music theory is sort of like learning the "grammar" (i.e. structural rules) of music.
People intuitively learn some of the "rules" of music merely by listening to a lot of music. It's much like a person learns their first language as a child. They may not be able to recite or explain the rules, but they will intuitively know what does and doesn't sound "correct" in their language by the time they begin formal education.
If a person learns to play an instrument (or sing), then they will probably become musically literate by learning musical notation, which is how music is written and read. It's like learning how to read and write in their language. Some people learn to play or sing by ear, without ever becoming musically literate.
Music theory is a deeper level of understanding. It's like studying a language academically. You can probably intuitively understand a lot of musical "grammar", but music theory teaches you how and why music sounds the way that it does. You learn the fundamentals of music and how they work in a meaningful way.
Some of the things you may learn in the study of music theory are:
- Musical Notation
- Melody, Harmony, and Rhythm
- Consonance and Dissonance
- Scales and Modes
- Chords and Chord Progression
- Musical Form/Structure
- Musical Analysis
- Sight-Reading
- Ear-Training
In an academic setting, courses in Music Theory - including Sight-Singing, Ear-Training and Musical Analysis as either integrated or separate courses - are generally part of a comprehensive musical curriculum including other musical studies such as Music History, Music Technology, Music Performance, Music Composition, etc. Most of these subjects complement and provide valuable context or synergy with each other.
If you want to begin learning music theory, I would suggest first learning the basics of musical notation, if you haven't already. There are a ton of websites that teach music notation as well as music theory. Here are a few.
A piano/keyboard (or even a guitar) is extremely useful for studying notation and music theory, because you can use it to visualize and play notes, chords, or anything else you are learning about.
There are virtual pianos you can use instead, on your computer/tablet/phone through websites or apps. They won't teach you play a real piano, but they will give you a useful visual of what you are studying.
You can take free university courses in music theory online. There are a plethora of really great lessons in music (and many other subjects) available online now. They run the gamut from blogs and YouTube tutorials all the way to actual Ivy League courses! Many universities are now offering selective course content online for anyone to learn through "Massive Open Online Courses" at sites like edX and Coursera.
Here are a some courses to get you started. Some are for true beginners, while others may require some basic skill or knowledge in music.
If you learn best from reading, it can be helpful to purchase textbooks and supplemental workbooks, if you can afford them. Don't be afraid to buy older editions! Older editions of textbooks are generally much cheaper, and the basics of classical music theory haven't really changed in a while. Newer editions are generally not a necessity in a subject like music. It's just a way for textbook publishers to milk more money out of college students.
You'll want to get staff paper at some point, for musical notation and theory exercises. (It's also called "manuscript paper" or even "blank sheet music".) There are plenty of sites that let you download & print free staff paper, or you can purchase notebooks of it. You can also use music notation software, but if you're still learning music notation it may feel unnecessarily complicated at first.
Useful Tools: