Getting all my emails online

Hi

I have many emails addresses with my domain name (webmail) + 2 gmail addresses.

I am looking for a "programme" from which I can receive and send all the emails from my multiple accounts from any browser and any computer.

I would like to be able to also import and keep all my email folders from stored on my mac mail so they are accessible online from anywhere in the world.

Is there such a "product"

Thank you