Ancient Greek lit for people who only mostly know what Greece is
My goal of this list is to give you an idea of what you want to read based on your interests and reasons for diving into Ancient Greek literature. Not to instruct you to read all of this stuff. I have only included things that have either survived in full or have significant amounts of surviving fragments and have public domain translations easily available to find online with minimal digging.
My advice though if you can afford it or find it at your local library is to go for the most recent translations of these works because those will likely be much easier to comprehend for your 21st century brain. It'll also likely be helpful for you to read translator's notes, footnotes, and introductions and read any maps included in your editions because those can often give you important historical and cultural context that may otherwise be confusing for you. The far past is another country so get all the context you feel that you need.
The basics aka what every Greek writer has also read and frequently references back to:
The Iliad and the Odyssey by Homer, stories of the mythical Trojan war and its aftermath. The Iliad is about the ending days of the war and focuses on the hero Achilles, while the Odyssey is about the hero Odysseus getting lost at sea for many years on his way home from the war.
The Theogony and Works and Days by Hesiod, an attempt at tracing the genealogy of the gods and other various myths and personal opinions about them. This is what most people use as reference when talking about Greek creation stories.
Other longer works about Mythology:
The Argonautica by Apollonius Rhodius, the story of Jason and the golden fleece and the adventures his sailing crew of heroes had on the way there.
The Library or Bibliotheca by Pseudo-Apollodorus, basically an ancient reference book on the stories of Greek religion, told in roughly chronological order.
The Dionysiaca by Nonnus, the longest surviving book of ancient Greek literature, it tells the story of the god Dionysus before he ascended to godhood and his trip to and return from India.
The Posthomerica by Quintus of Smyrna, likely written in the 3rd century AD, is an epic poem attempting to tell the parts of the fall of Troy that Homer left out between the death of the prince Hector and the burning of Troy.
The Homeric hymns, not actually by Homer but by an unknown author or authors, these are a series of short and long poems and songs that tell stories of various gods and also show a bit how they were worshiped.
The works of Sappho, though not much of her poetry has survived, what remains is still good. She mainly wrote love poems about women but also men and is notable for referring to herself in the first person, something which was unusual at the time.
The works of Pindar, probably the most well preserved of the "nine lyric poets" of ancient Greece his work has been seen as confusing and unusual at times, but it's still a treat to read in my opinion.
The works of Bacchylides, a contemporary of Pindar, but his poetry is thought to be much more understandable and approachable.
Plays about Mythology and Folklore, all tragedies:
The works of Sophocles, especially the Oedipus trilogy that includes Oedipus Rex, Oedipus at Colonus, and Antigone which tells the story of the king Oedipus who was doomed by an oracle and the aftermath of his actions on his family.
The works of Euripides, especially Medea about the witch Medea and her betrayal by the hero Jason and the Bacchae, which tells the story of the god Dionysus.
The works of Aeschylus, especially The Oresteia, which is a trilogy of plays including Agamemnon, The Libation Bearers, and The Eumenides which together tell the story of the murder of the Greek king Agamemnon, the consequences of the cycle of revenge that followed, and the pacification of the furies, who are goddesses of punishment.
Selected comedic plays and political satires which are all by Aristophanes because he's the one whose work survived:
The Birds, a comedy about a man who convinces local birds to build a city in the sky and replace the gods.
Thesmophoriazusae or, Women at the Thesmophoria, a comedy about a man who sneaks into a women's only festival where the women debate how to punish the playwright Euripides for something he's written. The play pokes fun at tragic playwrights and poets.
The Knights, a satire of Athenian political life and an open criticism of many real politicians at the time where the real politician Cleon is the villain of the story.
Famous works of philosophy, science, mathematics, and medicine:
The works of Plato, especially The Republic which is about his idea of a perfect society and The Symposium which discusses philosophy through imaginary dialogues with the philosopher Socrates.
The works of Aristotle, and depending on what you're interested in he has books on Ethics, Politics, Poetics, Physics, The Art of Rhetoric, and Metaphysics, usually titled by the subject they discuss.
Sayings and Anecdotes, attributed to Diogenes the Cynic, this is what survives of a work said to collect the sayings of the philosopher Diogenes and other philosophers of the school of Cynicism.
The Hippocratic Corpus, a collection of around 60 texts often attributed to the physician Hippocrates, though this has never been conclusively proven. Notable works in this collection include On Airs, Waters, and Places, Epidemics, On Ancient Medicine, and On the Sacred Disease.
The works of Euclid, especially The Elements, which is a treatise on geometry.
The works of Archimedes, a famous Greek mathematician, especially On the Sphere and Cylinder, Measurement of a Circle, The Method of Mechanical Theorums, and On Floating Bodies.
Enquiry into Plants by Theophrastus, a colleague of Aristotle who had significant influence on the early history of botany.
Histories, historical fiction, geographies, and travel guides. The line between these genres is extremely blurry in this time period:
Histories by Herodotus, an account of the Greco-Persian wars as well as stories collected from around the Mediterranean and observations Herodotus made himself in his travels.
History of the Peloponnesian War by Thucydides, an unfinished account of the Peloponnesian war between Athens and Sparta by an Athenian general. Often seen as unusually neutral and unbiased in his accounting of events for the time period, though it is sometimes unclear how accurate he is.
The works of Xenophon, a military leader and philosopher, especially Hellenica which picks up where Thucydides left off, Cyropaedia which is a (likely fictionalized) biography of Cyrus the Great, and Anabasis which tells the story of Cyrus the Younger's attempt to steal the Persian throne with the help of ten thousand Greek mercenaries.
Description of Greece by Pausanias, a description of parts of Roman era Greece including Pausanias' own experiences in his travels, various cities and religious sites, and descriptions of topography.
Histories by Polybius, a work that only survives partially, is by a Greek who lived in Rome for a time after capture and is one of our main literary sources on the Punic wars between Rome and Carthage.
The works of Plutarch, a priest at the temple of Apollo in Delphi during the Roman era, especially Parallel Lives, which is a collection of biographies of famous Greeks and Romans that Plutarch thought were similar, Life of Alexander, which is a biography of Alexander the Great, and Life of Caesar, which is a biography of Julius Caesar.
Okay that's what I have for you. Go have fun!