In terms of carbon dioxide release, which is the major driver of global warming, it's power generation by a long shot. Transportation is number two, manufacturing is number three. The largest emitter of methane, unsurprisingly, is the agricultural sector (i.e cows).

https://ourworldindata.org/emissions-by-sector

Fossil fuels probably, they're at the source at least.

The Oil Industry has hid their own climate change data from the public, lobbied to keep other industries dependent on fossil fuels.

When the oil industry saw that oil consumption was going down because of increased energy efficiency and moving away to renewable energy, they promoted use of more plastic, which is mostly made from crude oil.

Also, most fertilizer and pesticides are synthesized from crude oil. The so-called green revolution was entirely dependent on synthetic fertilizer and oil-derived pesticides. We're literally eating our oil.

Fuck oil companies!

This is a complex question. The obvious suspects are fossile fuels / power generation, but really that they are being consumed in great quantity is the problem. So then you have to evaluate which industry is consuming the most. Even that falls short though because there is a human value per unit power consumed factor to consider. Power consumed for heating homes or feeding people is probably more valuable than power consumed to drive yachts to Tahiti. We need fewer people; specifically rich people.

The United States military is one of the largest contributor to greenhouse gas emissions in the world

https://earth.org/us-military-pollution/

Historically, Big Autos and Big Oil/Big Fossil combined. Most recently with their AI datacenters sucking up all the water and also being powered by Big Oil/Big Fossil, Big Tech.

In fact, Big Autos, Big Oil, and Big Tech are tied for this one.

Agriculture

War

Entertainment industry. Just look what great lengths sports events do. With like the Olympics and the world cup, you have athletes, viewers and media all around the globe to travel to one country. For the world cup, you have teams travel quite some distances, especially with the last in North America. With something like Formular One, you have each team travel around the globe multiple times a year. You have so much events, where you have quite the amount who travel. And lets not forget, that they don't produce any value, just entertainment.

The coal industry

All industries support other indistries or produce stuff you consume.

You take away the oil industry you suddenly have no diesel for the agricultutal industry. Take away coal and you suddenly cripple the steel industry which just about every thing else is built of.

Thinking that just one industry causes climate destruction and no other useful output is a dead end.

Probably in the least compared to industrial, but I think Waste. Like landfills and all that.