Greek is the official language of Greece, where it is spoken by almost the entire population. It is also the official language of Cyprus (nominally alongside Turkish). Because of the membership of Greece and Cyprus in the European Union, Greek is one of the organization's 24 official languages.
Significant Greek-speaking communities exist in the USA, Australia, Albania, Italy, Ukraine, Turkey, Romania, and Hungary. Beyond these, Greek pops up in places all over the world.
Over 13 million people all over the world speak Greek. Around 11 million of them live in Greece, while the remaining 2 million or so live in other countries.
Unfortunately, no data is available on how many people in the world speak Greek as a second language. It may not be as popular a foreign language as English or Spanish, but it has a number of devoted fans and resources for learning it are freely available.
It may not be the most difficult language in the world to learn, but according to various studies, Greek is among the hardest languages for an English-speaking person to acquire. On the one hand, Greek is related to other European languages.
Things that may make Greek hard to master include: its alphabet, noun cases, verb conjugation system, inflections in other parts of speech, including articles. It is a grammatically heavy language, but it is also very logical and well-organized.
The Greek alphabet was developed about 1000 BCE, based on the Phoenician's North Semitic alphabet. It contains 24 letters including seven vowels. Originally, all of its letters were capitalized, lower case forms were developed much later than the upper-case ones.
While the Greek alphabet looks different, it is actually the forebear of the Latin and Cyrillic scripts.
A distinction is often made between Ancient and Modern Greek. Ancient Greek can be considered a dead language in the same way Old Slavonic or Old English are. There are no native speakers of these forms nowadays and speakers of the modern forms of these languages can hardly understand Old Slavonic, Old English or Ancient Greek.
Ancient Greek is a very old language. It has changed a lot since ancient times to become the Modern Greek we know today, which is a very much alive, spoken by over 13 million people all over the world.
Greek is the only language on its branch (Hellenic) of the Indo-European family tree, so it has no directly related languages. Its closest relations are said to be the Indo-Iranian languages, and Armenian, but that relation is nothing like the relationships that exist among the Romance, Germanic and Slavic languages.
A major language heavily influenced by Greek was Latin, with many words borrowed by the Romans. These words then passed into French, Italian, Spanish to name only three of the Romance languages.