All 5 Uses of

resolution
in
A Tale of Two Cities

Good-humoured looking on the whole, but implacable-looking, too; evidently a man of a strong resolution and a set purpose; a man not desirable to be met, rushing down a narrow pass with a gulf on either side, for nothing would turn the man.†
Chpt 1.5

He was now a very energetic man indeed, with great firmness of purpose, strength of resolution, and vigour of action.†
Chpt 2.10 *

This favoured the desperate resolution Charles Darnay had begun to make, that he would go to Paris.†
Chpt 2.24

As he walked to and fro with his resolution made, he considered that neither Lucie nor her father must know of it until he was gone.†
Chpt 2.24

Definitions:

(1) (resolution as in: a New Year's resolution)
a firm decision to do something
(2) (resolution as in: a United Nations resolution)
a formal statement of decision or opinion voted on by a group

While a resolution typically expresses an opinion and has no legal force, when used in early U.S. history or in the expressions joint resolution of Congress or continuing resolution, it becomes a synonym for legislation (meaning that it carries the force of law).
(3) (resolution as in: Her resolution weakened.)
determination (firmness of purpose)
(4) (resolution as in: resolution of the dispute)
a solution or outcome
(5) (meaning too rare to warrant focus)
meaning too rare to warrant focus:

Much less commonly, other meanings of resolution include:
- a measure of optic detail -- as in: "The photograph has excellent resolution."
- separation into different parts -- as in: "When force is applied to an inclined plane there is resolution of the force into horizontal and vertical components."
- conversion to something else -- as in: "... resolution of the chord from dissonance (an unstable sound) to consonance (a more stable sound)."
- reduction to or conversion to something else -- as in: "It permits resolution of a URL to an IP address."