The first alphabet came about 3700 years ago via the West Semitic people of the Sinai. They had become workers or slaves under the Egyptians and saw the hieroglyphs that were being used. Only the consonants in the hieroglyphs were recorded, no vowels, thus the Sinaitic script adopted the same format. The Egyptians used multi-consonant signs but Sinaitic used only single consonant letters.
The South Arabian family evolved at around 1300BC eventually becoming a highly elegant script by the 5th century BC. As Islam increased in popularity the script diffused across the Red Sea into Ethiopia and this is still used today.
The Phoenician alphabet evolved into a more linear form by the 12th century BC and most of the alphabets that are used today descend from this. The immediate offsprings were the old Hebrew alphabet and Archaic Greek. Aramaic became very popular and became an international language spoken from Anatolia all the way to the Persian Gulf. In Israel it became the Jewish alphabet.
Then, of course, we have the Greek and Latin scripts. No archeological remains have been discovered of the early Greek - examples only date from the 8th century BC but many scholars believe that it was adopted from the Phoenician between 1200 - 900 BC. The Euboean variant was transmitted to the Etruscans and so on to Latin.
Futhark and Ogham are both systems that were used in Northern Europe before being replaced by the Latin alphabet - the origins of these are still under debate.