These bindings correspond to the US keyboard layout. If you're using an international keyboard, some of the special symbols might be on different keys.

Before we get to the main shortcuts, a very useful one to know is:

ESC: Same as pressing the back button or menu if on the main screen.

Drawing tools:

B: Pencil
E: Eraser
G: Color fill
I: Color picker
H: Hand (move canvas)
L: Line
U: Rectangle (press U again for filled rectangle)
SHIFT+U: Ellipse (press SHIFT+U again for filled ellipse)

Some tools can be opened temporarily and will switch back to the previous tool when you let go of the key:

SPACE: Hand (move canvas)
ALT/OPTION: Color picker

Another key that you can hold is:

SHIFT: Pencil line drawing mode

With the pencil tool equipped, if you press SHIFT before you start drawing, a line will appear from the last drawn pixel to the current pixel. But if you first press the mouse down and then press SHIFT and move the mouse, it will constrain the pencil to draw a vertical or horizontal line, depending on which direction you move.

Other commands:

CTRL/CMD + Z: Undo
CTRL/CMD + Y: Redo (Windows style)
CTRL/CMD + SHIFT + Z: Redo (macOS style)

CTRL/CMD + =: Zoom in
CTRL/CMD + SHIFT + =: Zoom in
CTRL/CMD + NUMPAD PLUS: Zoom in
CTRL/CMD + -: Zoom out
CTRL/CMD + NUMPAD MINUS: Zoom out

=: Increase brush size
SHIFT + =: Increase brush size
NUMPAD PLUS: Increase brush size
-: Decrease brush size
NUMPAD MINUS: Decrease brush size

One undocumented extra:

F: Focus mode when drawing

It's also good to know what you can do with the mouse. Right and middle click will temporarily switch to different tools:

RIGHT CLICK: Eraser
MIDDLE CLICK: Hand (move canvas)

And you can also use the mouse wheel:

SCROLL: Zoom in/out

Through the settings, you can replace the right click to act as the back button instead (similar to pressing ESC).