The Invention of the Alphabet

Figure 1: From Egyptian to Phoenician Proto-Sinaitic Symbol (ca. 1700 BCE) Semitic Name English Meaning Approximate Sound Phoenician Symbol (ca. 700 BCE) 'aleph Ox glottal stop (catch in voice) beth House b gimel Throwing stick g in glory daleth Door d he Man praying, shouting  h waw Hook, peg w zayin  Ax z heth Fence  kh   teth Wheel   t' yod  Arm and hand y in yellow kaph Palm of hand k lamed Ox-goad l mem Water m nun Snake n   samekh  Fish s `ayin Eye voiced pharyngeal fricative (gagging sound) pe Mouth p tsadhe Papyrus plant ts qoph  Monkey rough k resh Head r shin Bow sh taw Mark  t

According to AncientScripts.com: Proto-Sinaitic, "Proto-Sinaitic, also known as Proto-Canaanite, was the first consonantal alphabet. Even a quick and cursory glance at its inventory of signs makes this script's Egyptian origin very apparent. Originally it was thought that at around 1700 BCE, Sinai was conquered by Egypt, and the local West-Semitic population was influenced by Egyptian culture and adopted a small number of hieroglyphic signs (about 30) to write their own language. However, recent discoveries in Egypt itself have compounded this scenario. Inscriptions dating to 1900 BCE written in what appears to be Proto-Sinaitic were found in Upper Egypt, and nearby Egyptian texts speak of the presence of Semitic-speaking people living in Egypt.
"No matter where and when the adoption of Egpytian signs onto a Semitic language occurred, the process of adoption is quite interesting. Egyptian hieroglyphs already have phonetic signs (in addition to logograms), but the Sinaitic people did not adopt these phonetic signs. Instead, they randomly chose pictorial Egyptian glyphs (like ox-head, house, etc), where each sign stood for a consonant. How did they decide which sign get which consonant? A sign is a picture of an object, and the first consonant of the word for this object becomes the sound the sign represents. In short, this is called the acrophonic principle.
"For example, the word for an ox is /'aleph/, which is the first sign on the left Proto-Sinaitic column. It stood for the sound /'/, which is the glottal stop (also written as /?/)."
During the Egyptian Middle Kingdom, foreign names, including Semitic names, were written in characters of only one consonant, in other words, alphabetically.  This may have inspired the Semitic adapter(s) (Sass).  The style observed in the 1999 find in Wadi el-Hol shows that the adoption took place around 2000 BCE, most likely in Egypt itself.  You can see examples of Proto-Sinaitic inscriptions at Middle Bronze Age Alphabets (WikiPedia)  and The Origins and Emergence of West Semitic Alphabetic Scripts . 
The Proto-Sinaitic alphabet moved north and the Phoenicians eventually adapted it by 1100 BCE.  By then it had become more stylized and simpler.  The order, which basically has been maintained to this day, was established by 1300 BCE.  The reason for the order is not known.  It may simply be the order in which the symbols were invented (Peter T. Daniels), or it may be based on an ancient calendar (Garbini). 
Note that the Proto-Sinaitic and Phoenician alphabets only write consonants, perhaps because the Egyptians had symbols for single consonants but not vowels.  The Greeks were to change this. 

Figure 2: From Phoenician to Greek

(Click here to see a version of this table that includes the Modern Hebrew script)

Phoenician Symbol (ca. 700 BCE)	Semitic Name	Approximate Semitic Sound	Euboean Greek Symbol (ca 700 BCE)	Ionian Greek Symbol (ca 700 BCE)	Modern Greek Symbol	Greek Name
	'aleph	glottal stop (catch in voice)				alpha
	beth	b				beta
	gimel	g in glory				gamma
	daleth	d				delta
	he	h				epsilon ("plain e")
	waw	w			---	digamma
	zayin	z				zeta
	heth					eta
	teth					theta
	yod	y in yellow				iota
	kaph	k				kappa
	lamed	l				lambda
	mem	m				mu
	nun	n				nu
	samekh	s				xi
	`ayin	pharyngeal consonant (gagging sound)				omicron ("little o')
	pe	p				pi
	tsadhe	ts			---	san
	qoph	rough k			---	qoppa
	resh	r				rho
	shin	sh				sigma
	taw	t				tau
	(waw)	w				upsilon ("plain y")
						phi
						chi
						xi (alternate)
						chi (alternate)
						psi
						omega ("big o")

The Greeks next adapted the Phoenician alphabet for their own use.  The date for this is controversial, but certainly no later than 800 BCE, although the place that this occured is unknown.    Bear in mind that while Phoenician was always written from right to left, ultimately Greek came to be written from left to right, as is our own Latin alphabet.  This explains many of the changes made to the Phoenician symbols in the Greek alphabet.  The Greeks rotated some characters, such as 'aleph  as alpha, and changed the shapes of others.   There had been many variations of the Phoenician characters in their development in any case. 
The great innovation of the Greeks was to provide letters for vowels as well as consonants, although this probably happened by accident rather than by design.   Most likely  the Greeks simply did not hear the beginning non-Greek consonants of the names for certain letters, so they assumed that the letters stood for vowels.  Thus  'aleph became alpha (a Greek word cannot end in a consonant, with few exceptions), he became e (later called epsilon, "plain e"), heth became heta, yod become iota,  and  `ayin became o (since this Semitic consonant is pronounced far back in the throat, the Greeks heard an "o";  this was later called omicron, "little o", that is "short o", in contrast to omega, "big o" that is, "long o".)   They adopted the rest of the names of the Phoenician characters with minor changes to make them more pronounceable.  Thus the Greeks invented the first true alphabet in history, the first to indicate both consonants and vowels independently and more or less completely.  
The Greeks used the Semitic waw in two places:  for digamma, which had the sound of the English consonant w, and for  upsilon, where it must have originally had the sound of oo in "moon".  Later the Greeks omitted digamma , although it had already made its way into the Latin alphabet as F.    The Greek language later changed so that the sound originally represented by upsilon changed to the vowel like German ü or French u in "du" .  They then used omicron-upsilon for the oo sound in "moon", much as French does.
San was an alternative for sigma for a while and then disappeared.  Qoppa, an alternative for kappa, also disappeared,  but not until it made its way into the Latin alphabet as Q .
To represent some sound distinctions made in Greek but not in Phoenician, the Greeks added phi, chi, psi, and later omega to the Phoenician symbols, listing these at the end.  It is not clear where they got these symbols, although omega seems to be omicron with the bottom opened. 
At the beginning there were different local versions of the Greek alphabet.  The version used in Ionia eventually became the standard one.  The version used in Euboea did not use the Phoenician symbol samekh  for xi (although it did list it), instead using the symbol like our letter X for the consonant group /ks/, and using  a symbol somewhat like psi for chi.  This is important, since it was the Euboean Greek alphabet that would  become the Latin alphabet.  

Figure 2a: From Phoenician to Modern Hebrew and Greek

Phoenician Symbol (ca. 700 BCE)	Modern Hebrew Symbol	Semitic Name	Approximate Semitic Sound	Greek Symbol (ca 700 BCE)	Modern Greek Symbol	Greek Name
		'aleph	glottal stop (catch in voice)			alpha
		beth	b			beta
		gimel	g in glory			gamma
		daleth	d			delta
		he	h			epsilon ("plain e")
		waw	w		---	digamma)
		zayin	z			zeta
		heth				eta
		teth				theta
		yod	y in yellow			iota
		kaph	k			kappa
		lamed	l			lambda
		mem	m			mu
		nun	n			nu
		samekh	s			xi
		`ayin	pharyngeal consonant (gagging sound)			omicron ("little o")
		pe	p			pi
		tsadhe	ts		---	san
		qoph	rough k		---	qoppa
		resh	r			rho
		shin	sh			sigma
		taw	t			tau
		waw	w			upsilon ("plain y")
						phi
						chi
						psi
						omega ("big o")

.

Figure 3: From Greek to Latin

Euboean Greek Symbol (ca 700 BCE)	Greek Name	Early Latin	Modern Latin	Notes
	alpha		A
	beta		B
	gamma		C
	delta		D
	epsilon		E
	digamma		F
			G	In the 3rd century BCE Spurius Carvilius Ruga created this from  C.
	zeta	See below		See at bottom
	eta		H	The Euboean Greeks used eta for the English sound h , which the Romans continued.
	theta	---		The Romans did not have this sound and did not use this character.
	iota		I
			J	From the 14th to the 17th centuries CE  scribes created J  to distinguish the semi-vowel English y from the vowel i.
	kappa		K	The Romans used K for a few names.
	lambda		L
	mu		M
	nu		N
	(Ionian xi)	---		The Etruscans listed this in their model alphabet but did not use it.  The Romans never adopted it.
	omicron		O
	pi		P
	san			The Etruscans had this redundant letter and sometimes used it but the Romans never adopted it.
	qoppa		Q
	rho		R
	sigma		S
	tau		T
			U	Around 100 CE the Romans created  this rounded form to stand solely for the vowel, and then  V stood for the semi-vowel alone.
	upsilon		V	This was the original Roman  form for both the vowel oo as in moon and the English semi-vowel w .
			W	Medieval scribes created this letter,  sometimes for our "v", sometimes for our "w" semi-vowel.
	phi			The Etruscans adopted this but the Romans did not need it.
	Euboean xi		X	The Euboian Greeks used this letter for the /ks/ combination.  The Etrusncans used it for something else, but the Romans adopted it with the Greek value.
			Y	Around the end of the Roman Republic,  Y was included at the end to transcribe upsilon in Greek loan-words.
			Z	Around the end of the Roman Republic,  Z was included at the end to transcribe zeta in Greek loan-words.
	Euboean chi/ Ionian psi			The Etruscans and Romans never adopted this letter.
	omega			The Etruscans and Romans never adopted this later Greek letter.

The Etruscans adopted the Greek alphabet from Greek colonies at Pithekoussai (on the island of Ischia) and Cumae.  In turn the Romans adopted their alphabet from the Etruscans.   The Etruscans abandonned the Greek letter names, calling the letters simply by their sounds, much as we do today. 
These Greek colonists  were from Euboea and thus  used their own  local version of the Greek alphabet at the time they colonized Italy.  One can see its influence where the Euboean gamma, delta, and sigma clearly resemble the modern Roman C, D, and S, which the Ionian forms do not.  The Euboean alphabet also used the X symbol rather than the Phoenician samekh for the consonant combination /ks/.   Since X did not come with the Phoenician alphabet, it was placed at the end.   (Most western Greek alphabets did not include the samekh symbol at all, but apparently the Euboean one did, since the Etruscans list it in their model alphabet, although they did not use it in practice.  The  Romans never even listed the samekh symbol.)  
The Greeks used the Semitic waw in two places:  for digamma, which has the consonant sound of English w, and in upsilon, where it originally had the sound of oo in "moon".  The Etruscans used F (digamma) for a /v/ sound and wrote our /f/ sound as FH.  The Romans simply used F for the sound we know.  Digamma disappeared after a while from the Greek alphabet itself.   Upsilon became the Etruscan and Roman V.  Later the Romans added the Greek upsilon itself at the end of the alphabet as Y to transcribe Greek loan-words.  
At first the Romans omitted zeta and placed the newly invented G in its place, and later they added zeta back in at the end of the alphabet to transcribe Greek loan-words. 
Qoppa, in Greek an alternative for kappa, made its way into Etruscan and Latin as Q, even though it then disappeared from the Greek alphabet.   The redundant letter san disappeared from Greek but made its way into the Etruscan alphabet, though not into the Latin one.