Of course, alphabet has to be of greek origin - alpha beta. It is the first two letters of the alphabet.
"letters of a language arranged in customary order," 1570s, from Late Latin alphabetum (Tertullian), from Greek alphabetos, from alpha + beta. Attested from early 15c. in a sense "learning or lore acquired through reading." Words for it in Old English included stæfræw, literally "row of letters," stæfrof "array of letters."
This is a long evolution to get to an alphabet. We think of the Egyptians and their hieroglyphics - there were around 800 characters growing to as many as 5,000 characters, and then simplifying things with the "publishing" of Hieroglyphic Bookhand. It remains one of the most complicated "alphabets" in history.
Early vowelless alphabets are called abjads and still exist in scripts such as Arabic, Hebrew, and Syriac. They are not considered proper alphabets.
Phoenician was the first major phonemic script. In contrast to two other widely used writing systems at the time, cuneiform and Egyptian hieroglyphs, it contained only about two dozen distinct letters, making it a script simple enough for common traders to learn. Another advantage of Phoenician was that it could be used to write down many different languages since it recorded words phonemically.
I am so impressed with scholars who were able to figure these out, and for archeologists who found that Egyptians wrote left to right and also in all directions. 
The Phoenician alphabet spread to the Italian peninsula, and gave rise to a variety of alphabets - of course one of these became the Latin alphabet. It was spread far and wide across the Roman Empire, explaining its enduring continuation, especially since it occurred in intellectual and religious works. No one was giving these up.
To get to the English alphabet takes a few giant steps - Old English, Middle English, and finally Modern English, starting in the mid 15th century. The first English dictionary was titled Table Alphabeticall.
Here's a humorous story:
It was a wise though a lazy cleric whom Luther mentions in his "Table Talk," — the monk who, instead of reciting his breviary, used to run over the alphabet and then say, "O my God, take this alphabet, and put it together how you will." [William S. Walsh, "Handy-Book of Literary Curiosities," 1892]
Here's some advice:
If "Plan A" didn't work, the alphabet has 25 more letters.
Here's the injection of mathematics into things:
I was good at math until they mixed the alphabet into it.
Today we have more pictures from the Fantasy of Trees display.
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