The following keyboard shortcuts are available in both iOS and OSX versions (unless indicated otherwise.)

NB: iOS requires bluetooth keyboard

TAB Create a new child
RETURN End edit or create new sibling
CMD+RETURN Start edit or create a new sibling (splitting the text at the cursor if necessary)
SHIFT+RETURN Create a new sibling (before)
ALT+RETURN Insert newline into topic text
SHIFT+TAB Create new parent
F2 [OSX only] Edit selected topic text
PERIOD Show/Hide a branch
[0..9] Show N levels or sub topic deep
CMD [1..5] Set topic priority
ALT [1..9] Add nth favourite icon
SPACE Show QuickLook (images/attachments)
ESC Abort edit and revert to original text or deselect all. Undo is available to recover any reverted text.
CMD+A Select All (visible) topics
Arrow Key Navigate around the map (topic to topic)
CMD+Arrow Key Change topic order
ALT+Arrow Key Nudge manual aligned topic positions
CMD+ALT+Arrow Key Create new related floating topics
CMD+[X C V] Cut/ Copy/ Paste
BACKSPACE Delete selected topics (including child topics)
CMD+BACKSPACE Delete individual (selected) topics (not including child topics)
CMD +/- Increase/decrease size (image, font etc.)
CMD+[B I U] Bold/ Italic/ Underline
CMD+ALT+U Strikethrough
CMD+F [OSX only] Find/Replace
CMD+SHIFT+T Toggle the notes window open/closed
CMD+CTRL+T Toggle between editing note and topic text
CMD+R Research - launch browser with topic text as search term
CTRL+CMD+F Toggle 'full screen' mode
CMD+SHIFT+K Insert Callout topic
L [OSX only] Create relationship between 2 selected topics
CMD+0 Toggle between 'Zoom to fit map' and 'Center map with no zoom'
CMD+SHIFT+0 Toggle between 'Zoom to fit map' and 'Zoom to fit selection'
CMD+CTRL+0 Toggle 'auto zoom' on/off
CMD+> Zoom in
CMD+< Zoom out
P Increment the Progress attribute (SHIFT+P to decrement)
CMD+K [OSX only] Edit the hyperlink attribute
CMD+ALT+K Open the hyperlink
CMD+SHIFT+F Toggle Focus mode on/off
DoubleClick Canvas Create new floating topic (DoubleTap on iOS)
CMD+DoubleClick Canvas Create new related floating topic (SHIFT+DoubleTap on iOS)
CMD+DoubleClick Topic Create new relationship (SHIFT+DoubleTap on iOS)