If you are transitioning from windows, then in order of preference you will probably want to use, evim, gvim, vim.
evim makes gvim behave like windows editors (note Ctrl+L gets you to vim Normal mode). If one just wants the windows key mappings from evim mode in gvim for e.g. you can use the following command: source $VIMRUNTIME/mswin.vim. Other alternatives if you're transitioning from windows are nedit or geany.

If you're stuck with text mode access, then vim is probably the best option, so you need this info (all of which also applies to gvim and evim). Another reason that it is good to know this is that many programs use vim key bindings. For e.g. the readline library can be configured to use vi bindings and hence this info will be useful to you in bash, ftp,gnuplot,python,bc,... Also less (used to read man pages on Linux) defaults to vi key bindings.

Note most commands take an optional number (of times to run) on front
(e.g. 3. repeats the last action 3 times, or 3w moves forward 3 words etc.).

Here are my vim settings and my gvim settings.

vim file +54open file and go to line 54any : command can be run using + on command line
vim -O file1 file2open file1 and file2 side by side 
Insertenter insert modeso you can start typing. Alternatively one can use i or a.
Escleave insert modeso you can issue commands. Note in VIM the cursor keys & {Home, End, Page{up,down}} and Delete and Backspace work as expected in any mode, so you don't need to go back to command mode nearly as much as the origonal vi. Note even Ctrl+{left,right} jumps words like most other editors. Note also Ctrl+[ and Ctrl+c are equivalent to Esc and may be easier to type. Also Ctrl+o in insert mode will switch to normal mode for one command only and automatically switch back.
:commandruns named command 
:help wordshows help on wordTyping Ctrl+d after word shows all entries containing word
:echo &wordshows value of word 
:eset buffer for current windowyou can optionally specify a new file or existing buffer number (#3 for e.g.). Note if you specify a directory a file browser is started. E.g. :e . will start the browser in the current directory (which can be changed with the :cd command).
:spnew window aboveditto
:vsnew window to leftditto
:qclose current window 
:qaclose all windowsadd trailing ! to force
Ctrl+w {left,right,up,down}move to window 
Ctrl+w Ctrl+wtoggle window focus 
Ctrl+w =autosize windowsto new terminal size for e.g.
:banew window for all buffers":vert ba" tiles windows vertically
:lslist buffers 
gfopen file under cursor 
:bddelete bufferand any associated windows
:wsave fileNote :up[date] only writes file if changes made, but it's more awkward to type
:sav filenamesave file as filenameNote :w filename doesn't switch to new file. Subsequent edits/saves happen to existing file
ggGoto start of file 
GGoto end of file 
:54Goto line 54 
80|Goto column 80 
Ctrl+gShow file infoincluding your position in the file
gaShow character infog8 shows UTF8 encoding
Ctrl+escroll upCtrl+x needed first for insert mode
Ctrl+yscroll downCtrl+x needed first for insert mode
ztscroll current line to top of window 
wGoto next wordNote Ctrl+{right} in newer vims (which work also in insert mode)
bGoto previous wordNote Ctrl+{left} in newer vims
[{Goto previous { of current scope 
%Goto matching #if #else,{},(),[],/* */must be one on line
zitoggle folds on/off 
m {a-z}mark position as {a-z}E.g. m a
' {a-z}move to position {a-z}E.g. ' a
' 'move to previous position 
'0open previous filehandy after starting vim
vselect visuallyuse cursor keys, home, end etc.
Shift+vline selectCTRL+v = column select
Deletecut selection 
"_xdelete selectionwithout updating the clipboard or yank buffer.
I remap x to this in my .vimrc
ycopy selection 
ppaste (after cursor)P is paste before cursor
"Ayappend selected lines to register ause lowercase a to initialise register
"appaste contents of a 
gqreformat selectionjustifies text and is useful with :set textwidth=70 (80 is default)
=reindent selectionvery useful to fix indentation for c code
>indent sectionuseful with Shift+v%
<unindent sectionremember . to repeat and u to undo
:set list!toggle visible whitespaceSee also listchars in my .vimrc
clipboard shortcuts
ddcut current line 
yycopy current line 
Dcut to end of line 
y$copy to end of line 
/regexpsearches forwards for regexp? reverses direction
nrepeat previous searchN reverses direction
*searches forward for word under cursor# reverses direction
:%s/1/2/gcsearch for regexp 1 and
replace with 2 in file
c = confirm change
:s/1/2/gsearch for regexp 1 and
replace with 2 in (visual) selection
Klookup word under cursor in man pages2K means lookup in section 2
:makerun make in current directory 
Ctrl+]jump to tagCtrl+t to jump back levels. I map these to Alt+⇦⇨ in my .vimrc
vim -t nameStart editing where name is defined 
Ctrl+{n,p}scroll forward,back through
autocompletions for
word before cursor
uses words in current file (and included files) by default. You can change to a dictionary for e.g:
set complete=k/usr/share/dicts/words
Note only works in insert mode
Ctrl+x Ctrl+oscroll through
language specific completions for
text before cursor
"Intellisense" for vim (7 & later).
:help compl-omni for more info.
Useful for python, css, javascript, ctags, ...
Note only works in insert mode
external filters
:%!filterput whole file through filter 
:!filterput (visual) selection through filter 
:,!commandreplace current line with command output 
map <f9> :w<CR>:!python %<CR>run current file with external program 
© Jul 12 2007