Gmail's keyboard shortcuts are off by default — turn them on first at Settings > See all settings > General > Keyboard shortcuts > On > Save Changes. Once enabled, they work whenever your cursor isn't inside a text field.

General
ShortcutWhat it does
cCompose a new message
/Jump to the search bar
?Show the full shortcuts list
g then iGo to Inbox
g then sGo to Starred
g then tGo to Sent
g then dGo to Drafts
Managing mail
ShortcutWhat it does
eArchive
#Delete
!Report as spam
lApply a label
mMute the conversation
zUndo the last action
Navigating between messages
ShortcutWhat it does
j / kMove to the next / previous conversation
o or EnterOpen the selected conversation
uBack to the inbox list
Composing & replying
ShortcutWhat it does
rReply
aReply all
fForward
Ctrl + Enter (Cmd + Enter on Mac)Send
Selecting
ShortcutWhat it does
xSelect the conversation
Shift + uMark as unread

These are browser shortcuts, so they’re identical on Windows and Mac except for sending a message: use Cmd+Enter on a Mac where the sheet says Ctrl+Enter.