Reddit reviews Classical World: An Epic History From Homer To Hadrian

It depends how 'academic' you want to go.

For a great 'pop' history of the entire Classical world, a good bet might be Robin Lane Fox's The Classical World, which is very readable and includes both Greece and Rome.

For something more recent, Edith Hall's Introducing the Ancient Greeks is really excellent, and (since it was only released a couple of years ago) is very up-to-date with the latest scholarship. (There is plenty of new evidence on what was happening in Greece between c.1200-700 BCE, for example).

If you want something more 'academic', Robin Osborne's Greece in the Making, 1200-479 BC and Simon Hornblower's The Greek World, 479-323 BC will take you from the collapse of Mycenaean civilisation to the death of Alexander. Both of these are pretty in-depth accounts written by serious historians, and are also a little bit older.

I always recommend books, between them is The Classical World, by Robin Lane Fox https://www.amazon.co.uk/Classical-World-Epic-History-Greece/dp/0141021411

Also this massive list: https://bonesandcoffeemugs.tumblr.com/post/186695189213/can-you-recommend-some-books-or-somethung-else-to