Here's a full list of Keyboard Hotkeys:

Setting Menu Delay to 1 enables the 'Classic' mode, right click opens a menu.
Setting Menu Delay to anything else enables the 'Updated' mode, right click either moves or attacks. right-click and hold opens a menu.
Mouse Drags now works in most places like a right click.
Double-click on an enemy unit optionally opens up the combat planner dialog.
Left mouse click on some dialogs hides the dialog so you can see the map.

Mousewheel or extra mouse buttons - zoom the map in and out.
Escape or Enter - Closes most dialogs
F1 - Opens the manual
F2 - Open the Group Composition dialog
F3 - Saves Map
F4 - If in OOB, saves OOB for both sides
F4 Shift Ctrl - saves OOB for current player
F5 - If in OOB, reads OOB for both sides
F6 - If not playing saves event file
F7 - If not playing loads event file
F8 - If not playing saves scenraio as 3.2
F9 - If playing does a quick save
F11 - Creates a NewGameText.xml file
F12 or \-Toggles Elmer Deployment Mode
Shift F12 or | Elmer moves your units
Arrow Keys - Move map
Ctrl Arrow Keys - Move micro map
Center Numpad Key Centers Map on Unit

1-9 Selects that entry on a dialog that has the entries above each other.
Space - Shows/Hides units for terrain analysis. Also hides some dialogs so you can see the map.
A - List Air Units
A/Shift - Air List
B - Find Place
B/Ctrl - Find Next Place
C - Group Composition dialog
D - Dig in
E - End Turn
F - Formation dialog
G - Selects next unit in stack
H - Moves HQs to top of stacks, second time  moves Artillery to tops of stacks
I - Toggles through the range circles options
J - Brings up the Jump Map [Esc to exit the Jump Map]
L - Toggle through loss limit settings
L/Shift - Toggle the stack through loss limit settings
M - Shows remaining movement or attack/defense strength
N/+ - Next Unit
- - Previous unit
O - Brings up OOB (list of all Units)
P - Brings up combat planner
R - Refresh the display of the current unit
T - Tactical reserve mode
T/Shift - Theater options
U - Unit Report
W - Toggle Weather On/Off
Y - Map Zoom [in]
Y/Shift - Map Zoom [if you had zoomed in, this will zoom out]
Z - Undo
. - Disembarks the unit if embarked, else goes to next unit.
, - Integrates or splits units
/ Show current formation path
? Show all formation paths
Ctrl + R - Resets Graphics. 

 Editor Hotkeys
A - If in Editor OOB, Copy unit equipment
G - If in Editor OOB, Paste unit equipment [used to replace the equipment in another unit]
F4 – Saves the current Order of Battle as a specially formatted text file.
F5 – Loads a specially-formatted text file as an order of battle.
F6 – Saves the current Scenario’s Event List as a specially formatted text file.
F7 – Loads a specially-formatted text file as the Event List of the current Scenario.
F8 – Saves the scenario in TOAW III version 3.4 format.
<Shift> and F8 – Saves the scenario in TOAW III version 3.2 format.
F11 – Regenerates the .eqp and .nqp files.
Ctrl + R - Resets Graphics. 
X - Creates a 'Unit Color Text Dump' XML file. 

The effects of right or left mouse clicks are usually different and are always described in the Information Panel at the bottom of the screen or window. When you first start the game, you may find it helpful to slowly pass the mouse cursor over the entire Game Window while keeping an eye on the Information Panel near the bottom of the display. As you play, keep an eye on the Information Panel for prompts and information.