Use only the abbreviations that fit your needs and that you will remember easily. A good idea is to introduce only a few abbreviations into your note taking at a time.

Symbols helpful in math -- these are commonly used in texts and references.
S = sum
f = frequency

Leave out periods in standard abbreviations.
cf = compare
e.g. = example
dept = department

Use only the first syllable of a word.
pol = politics
dem = democracy
lib = liberal
cap = capitalism

Use entire first syllable and only 1st letter of 2nd syllable.
pres = presentation
subj = subject
ind = individual
cons = conservative

Eliminate final letters. Use just enough of the word to form a recognizable abbreviation.
assoc = associate
biol = biology
info = information
ach = achievement
chem = chemistry
max = maximum
intro = introduction
conc = concentration
min = minimum
rep = repetition

Omit vowels, retain only enough consonants to give a recognizable skeleton of the word.
ppd = prepared
prblm = problem
estmt = estimate
bkgd = background
gvt = government

Use an apostrophe in place of letters.
am’t = amount
cont’d = continued
gov’t = government
educat’l = educational

Form the plural of a symbol or abbreviated word by adding s.
chpts = chapters
egs = examples
fs = frequencies
intros = introductions

Use g to represent ing endings.
ckg = checking
estg = establishing
decrg = decreasing
exptg = experimenting

Spell out short words such as in, at, to, but, for, and key.

Abbreviations or symbols for short words will make the notes too dense with shorthand.

Leave out unimportant words.
Leave out the words a and the.

If a term, phrase, or name is written out in full during the lecture, substitute initials whenever the term, phrase, or name is used again. For example, Center for Aerospace Sciences becomes CAS thereafter.

Use symbols for commonly recurring connective or transitional words.
& = and
w/ = with
w/o = without
vs = against
\ = therefore
= = is or equal

Use technical symbols where applicable.
zb = German, for example
ibid = Latin, the same work
o = degrees
H2O = water

From: The University Learning Center Resource File, 1997