Your (e.g., preparing for graduate school, data science, physics, or pure curiosity)
Real analysis is the rigorous foundation of calculus. It is where you truly understand what a limit is and why a function is continuous.
"Higher Algebra" does not mean solving for $x$; it refers to Abstract (or Modern) Algebra, which studies the symmetries and structures underlying numbers and shapes.
Many high-quality, peer-reviewed higher mathematics books are available for free online, especially for classic texts.
Do not jump into Baby Rudin without a solid grasp of proof techniques. Start with Velleman or Hammack first.