In which order do I need to learn chess to improve my rating

In which order do I need to learn chess to improve my rating?

To clarify, the rating is the consequence of results and not necessarily of understanding. There are thousands of players who get results in blitz and bullet because they've worked in opening theory and tactics, but can't replicate the results in OTB.

Why not? Because relying on opening and tactics preparation works when the rival isn't prepared or up to the task. This may happen even between strong players when just a few seconds to solve the problems. However, if time is not an issue, most can see through and find accurate solutions to evident and concrete problems.

There are two main roads to overcome the issue of the rival seeing through anything you throw at him: Really complicated problems (usually referred to as tactical play), and long term problems (usually referred to as positional play). Whatever the case, both are based on the balance of activity for both sides, which in turn depends on coordination (working as a unit when attacking or defending) and harmonious disposition of pieces and pawns (working as a unit that both attacks and defends).

In the end, it's all about making your pieces better than the rivals. And this is critical in endings. Then, if you want to increase your ratings as soon as possible, then a mix of tactics and openings will do. But if you want to increase your understanding of the game, and the ratings following as a consequence, then you should study endings, with attention to how the masters try to place their pieces to break or hold the balance of activity.