The word abbreviation comes from the Latin verb abbreviare with the adjective brevis, which means short. When you abbreviate something, you make it shorter.

Many abbreviations are formed by leaving out all except the first few letters of a word. These abbreviations often end with a full stop.

abstr.abstract
ad., advert.advertisement
admin.administration
approx.approximately
betw.between
cont.continue, continued
doc.document
esp.especially
est.estimated
etc.et cetera
examexamination
fig.figure
fut.future
infoinformation
introintroduction
lab.laboratory
lang.language
memomemorandum
min.minimum, minute
misc.miscellaneous
mod.modern
obs.obsolete
orig.origin, original(ly)
pop.popular
St.Street
tel.telephone
temp.temperature, temporary
vol.volume

Names of the months are abbreviated according to this general principle of just shortening words.

Jan.January
Feb.February
Mar.March
Apr.April
MayMay
Jun.June
Jul.July
Aug.August
Sep. or Sept.September
Oct.October
Nov.November
Dec.December

There is more variation in how the days of the week are abbreviated.

Mon.Monday
Tu., Tue. or Tues.Tuesday
Wed.Wednesday
Th., Thu., Thur. or Thurs.Thursday
Fri.Friday
Sat.Saturday
Sun.Sunday

Many abbreviations leave out letters in the middle of a word and end with the last letter of the word. Here are some examples:

apt.apartment
attn.attention
atty.attorney
dept.department
fwdforward
govt.government
hr.hour
Jr.junior
Ltd.Limited
mfg.manufacturing
mgmt.management
qty.quantity
tsp.teaspoon
yd.yard
yr.year

Some titles also follow this principle:

Dr.Doctor
MessrsPlural of Mr
MrMister
MrsMistress
MsgrMonsignor
St.Saint

You can read more about titles here.

Geographical names are often abbreviated:

Cambr.Cambridge
E. Afr.East Africa
Scand.Scandinavia
TXTexas
Victoria Rd.Victoria Road

Names of the states in the USA are abbreviated to two uppercase letters. You can find them here. The capital Washington is in the District of Columbia, abbreviated DC.

Abbreviations can also become words in their own right and we no longer realise that they are abbreviations.

Hankie (or hanky) is short for handkerchief.

The American colloquialism nabe comes from neighborhood.

Pram is short for perambulator, a carriage for a baby.

Soccer is an abbreviation of association football, which is different from American football.

Two girls lying on the grass watching a soccer game.
The girls were watching a soccer game

In American English abbreviations are usually followed by a full stop. In British English this generally applies to abbreviations that are formed by the first letter or the first few letters of a word as in the first table above.

There are many Latin abbreviations in the English language, which you can read about here and here.

Acronyms and initialisms are also abbreviations. Read about them here.