Deleting
x delete character under the cursor (short for "dl")
X delete character before the cursor (short for "dh")
dw (Delete Word Ex. dw,3dw,d3w,3d2w,d$,d^,df> )
dd (Delete Line Ex. dd,3dd)
D (Delete up to end of line. )(short for "d$")
diw delete word under the cursor (excluding white space)
daw delete word under the cursor (including white space)
dG delete until the end of the file
dgg delete until the start of the file

Arthemetic
CTRL-A Incrmenting Number (123, 0177, 0x1f,-98)
CTRL-X Decrementing Number

:set nrformats=""

Changing Text
cw (Change Word Ex cw,c2w)
C stands for c$ (change to end of the line)
s stands for cl (change one character)
S stands for cc (change a whole line)

The . Command
It repeats the last delete or change command.

Joining Lines
J (Join Lines to One. Ex J,3J)
gJ (Join Lines without Spaces)

Replacing Charcter
r (Replace Charater Under Cursour. Ex. ru,5ra,3r )
R

Changing Case
~ (Change Case of Character Ex. ~,12~,~fq)
U (Make the text Uppercase)
u (Make the text Lowercase)
g~motion (It does not depend on tildeop)
g~~ or g~g~ (Changes case of whole line)
gUmotion (All uppercase)
gUU (Changes to uppercase for whole line)
gUw (Changes to uppercase for word)
guw (Changes to lowercase for word)