What is the purpose of the yellow vest movement in France?

The yellow vest movement takes its name from the gilets jaunes, which are safety vests, that the protesters wear. French law requires motorists to carry such vests in their vehicles. Beginning in the provinces, the initial protests were led by drivers who put on the vests and created roadblocks. As the movement gained steam and spread to urban streets, especially in Paris, all the participants began to wear the vests. While there has been violence, many protests remain peaceful.
Beginning in November 2018, the demonstrators opposed a fuel tax that President Macron announced would be imposed starting January 1, 2019. By early December, the official government estimates reached almost half a million protestors, though participants say the numbers are much higher. They reject Macron’s claim that the tax is a “green” or ecological measure that will lead to decreased driving, thereby reducing gasoline and diesel usage and air pollution. Especially those who live in rural areas, have low incomes, and must drive long distances to work pointed out that the tax would unfairly impact them. From there, the movement has grown to encompass the working poor and middle class, who have seen their incomes and/or purchasing power shrinking in recent years.
Accusing Macron of being rich himself and of disproportionately favoring the rich through income tax cuts for the wealthy, some protestors call for his resignation or that of the National Assembly (similar to Congress), with the members to be replaced through new elections. More generally, along with a repeal of the tax, most call for an increase in the minimum wage.