I haven't really dug much into ancient egyptian history because i've had the impression of it as a relatively isolated culture that didn't leave the world much of a heritage (besides the obvious...) Now that's just my untaught impression; could someone point something out for me?
Very much so! I will only speak to one aspect in this post, although there are many. Our alphabet (i.e. the Latin alphabet) derives from Egyptian hieroglyphs.
The Egyptians had a very complex system of written language in which certain images depicted certain words. Sometimes, certain strings of images depicted a specific concept. It took tremendous dedication to learn the system, which is why the scribal class was a class. It took a lifetime of dedicated learning to master the language and then ensure that it could be passed on to the next generation.
The Phoenicians, who did not comprise a single nation but a geographic region of city-states named so by the Greeks, transformed Egyptian hieroglyphs into letters. After the mass collapse of the Late Bronze Age City States (ca. 1200 B.C.E.), former Canaanite peoples began migrating north to settle along the coast of what is today modern Lebanon. The ancient Palestinian (and modern for the matter) coast is very straight. It does not provide any natural breaks for harbors. The coast of modern Lebanon, however, is very accessible. These people, as they began to recollect, joined with other groups who were already there and established very strong cities. Written language is a near necessity for maritime trade, and these people began to develop their own quasi-hieroglyphic system. Eventually, someone had the genius idea to equate one consonantal sound with a single image. So whereas the 'bet' symbol had represented a house in hieroglyphs, the 'bet' symbol represented a 'b' sound. This way, the number of symbols one must master dropped by the hundreds if not thousands.
The Phoenicians traded with Egypt but also with the Aegean peoples, such as the Greeks. The Greeks actually adopted this alphabet, adding vowels whereas the Phoenician alphabet only included consonants (like Modern Hebrew today, speakers know where to add the vowels when vocalizing the language).
The Greeks colonized Rome before these colonies were eventually taken over by the Romans, but not before the Greek alphabet influenced the development of the Latin alphabet.
This is a long story, but we are indebted to the Egyptians for the alphabet that we use today. To go a bit more in-depth into the development of writing, I would suggest Joseph Naveh's, Early History of the Alphabet.
We get our current 365-day calendar, complete with leap days, from the Egyptians, via Julius Caesar and Pope Gregory XIII.
Before Julius Caesar, the Roman year was 355 days long, based on 12 months of 29 and 31 days (seven 29-day months and five 31-day months). Every second year, they added an intercalary month of 22 days during the month of Februarius to make up the difference.
Except... the responsibility for adding the Mensis Intercalaris fell on the College of Pontifices - the College of Priests of Rome. And, they were all sorts of unreliable, ranging from distracted and forgetful to political and malicious. Some years they simply forgot to add the Mensis Intercalaris, some years they were distracted by things like wars, and other years they deliberately didn't add the leap-month because they didn't like the consuls of the current year, so didn't want to give them an extra 22 days in office. After a few centuries of this, the Roman calendar was quite out of line with the seasons (when Caesar fixed things up, he had to add 90 days to one year to fix things up).
Caesar had spent some time in Egypt the year before his calendar reforms in Rome. (He couldn't have been there for much longer than a month, but Cleopatra gave birth to a son about nine months later who she called Caesarion, and who she claimed was Caesar's son. Appian wrote two hundred years later that "[Caesar] made a voyage on the Nile to look at the country with a flotilla of 400 ships in the company of Cleopatra, and enjoyed himself with her in other ways as well." Caesar never officially acknowledged the boy as his son, but never denied Cleopatra's story, either. Ahem.) The Egyptians had been using a strict 365-day year for thousands of years before this time. It fell one full day short of the seasons every 4 years, and cycled through the seasons every 1,460 years. (Over that millennium-and-a-half period, the New Year would gradually get earlier and earlier compared to the seasons until it eventually ended up back where it started!) A couple of hundred years before Caesar's time, the Ptolemaic rulers of Egypt had decreed that every fourth year should have an extra day added to it to keep the calendar aligned with the seasons, but the Egyptians weren't having a bar of it: the Egyptians knew when the seasons where, regardless of what the calendar might say, and didn't need some Greek kings who had only been in Egypt for a few decades telling them any different. Anyway, Caesar probably met some officials and priests on his tour of Egypt who told him about leap days.
When he returned to Rome, he instituted a similar system there: he changed the number of days in various months to increase the total to 365 days, he removed the Mensis Intercalaris, and he added a leap day to Februarius every four years.
That became the Julian calendar, which was used in Europe for over 1,500 years until it was further refined by Pope Gregory XIII to become the modern Gregorian calendar we all use.