Put this into your .bashrc to auto-start a tmux session after SSH login

auto-start-tmux-ssh.txt

# Put these lines into your server's .bashrc:
##
## TMUX auto attach
##
if [ -n "$SSH_CLIENT" ] || [ -n "$SSH_TTY" ]; then  # If this is an SSH session
  if which tmux >/dev/null 2>&1; then               # Check if tmux is installed
    if [[ -z "$TMUX" ]] ;then                       # Do not allow "tmux in tmux"
      ID="$( tmux ls | cut -d: -f1 | head -n 1 )"   # Get the id of an existing session
      if [[ -z "$ID" ]] ;then                       # If not available create a new one
        tmux new-session
      else
        tmux attach-session -t "$ID"                # If available, attach to it
      fi
    fi
  fi
fi