Reddit reviews The Art of Control Engineering

Start with classical control

• ODE, Laplace theory
  
• 1^st and 2^nd order systems
  
• Poles and zeros, feedback, stability (Root Locus, etc)
  
• System type and order, steady state errors
  
• PID
  
  That is represents a basic set of topics to properly understand linear systems. However, since we know that systems are not linear and implemented using computers (discrete-time control), this is just the beginning. It would probably take 6 months to learn the linear stuff given a reasonable foundation of mathematical knowledge. Depending on your preference and leaning when it comes to theoretical vs practical knowledge, I would suggest looking at Nise - Control Systems Engineering, which is more inline with the American, theoretical style or Dutton - The Art of Control Engineering, which more in keeping with the UK style of application.