Views:
Controls overview: F1
3rd person: V / ALT + SCROLL MMB
HUD: TAB
Signals: H
Terminal: K
Inventory/GPS/Factions/Production/etc.: I

Character controls:
Movement: WASD / QE / SPACE / C / SHIFT...
Jetpack: X
Inertia dampeners: Y or Z
Flashlight: L
Helmet visor: J
Broadcast position: O
Walk: Caps lock

Building:
Blocks: G
Toolbar switch: CTRL + 123...
Placement mode: B
Rotate block: INS/DEL/HOME/END/PGUP/PGDN
Block distance: CTRL + SCROLL MMB
Block variants: SCROLL MMB
Change block size: Press tool bar block button again
Delete grid: CTRL + DELETE
Building block line: CTRL + LMB DRAG
Building block square: CTRL + SHIFT + LMB DRAG

Admin:
Admin tools: ALT + F10 (creative mode tools, teleport, invulnerabe, remove entities, set time, weather, etc...)
Spawn menu: SHIFT + F10
Players promotion: F3

For hosting a multiplayer game with friends in survival mode with creative tools enabled:
Host player promote friends (F3)
Host player set up a faction and other players join this faction (I)
In Admin tools enable show all players + creative mode tools (ALT + F10)

Teleport to object/player:
ALT + F10 for admin tools
Cycle objects (players) or Entity list (planets/grids)
Teleport here
F6 to control player again

Teleport anywhere:
F8 to go to spectator mode
SHIFT + SCROLL MMB to change spectator speed
CTRL + SCROLL MMB to change spectator cam rotation sensitivity
CTRL + SPACE to place player to the spectator location
F6 to control player again

Blueprints:
F10 to save copied or paste saved blueprints
CTRL + C to create and copy a blueprint (with a block in hand, aimed at the target grid)
CTRL + V to paste a copied blueprint
B to align blueprint to the surface before pasting

Colors:
Color picker: P
Copy color: SHIFT + P
Paint 1 block: MMB click
Paint 3x3 blocks: Ctrl + MMB click
Paint 5x5 blocks: Shift + MMB click
Paint whole grid: Ctrl + Shift + MMB click

Symmetry building:
N turn on symmetry plane editing
M to turn on symmetry mode and to cycle between symmetry planes
CLICK LMB to place symmetry plane
N to verify block position
N to duplicate the block based on symmetry plane

Ship control set up (in ship cockpit):
K to open terminal and set up control groups
G to open parts
Drag controls to ship toolbar

Ship Controls:
Movement: WASD / QE / SPACE / C / ARROWS...
Inertia dampeners: Y or Z
Parking: P

Misc:
FPS meter: SHIFT + F11
Screen shot: F4
Save files location: %AppData%\SpaceEngineers\

Also make sure to enable Options/Game/Enable Cloud, to save/recover stuff via cloud saves.

Have fun!