The Sumerians were one of the earliest urban societies to emerge in the world, in Southern Mesopotamia more than 5000 years ago. They developed a writing system whose wedge-shaped strokes would influence the style of scripts in the same geographical area for the next 3000 years. Eventually, all of these diverse writing systems, which encompass both logophonetic, consonantal alphabetic, and syllabic systems, became known as cuneiform.
It is actually possible to trace the long road of the invention of the Sumerian writing system. For 5000 years before the appearance of writing in Mesopotamia, there were small clay objects in abstract shapes, called clay tokens, that were apparently used for counting agricultural and manufactured goods. As time went by, the ancient Mesopotamians realized that they needed a way to keep all the clay tokens securely together (to prevent loss, theft, etc), so they started putting multiple clay tokens into a large, hollow clay container which they then sealed up. However, once sealed, the problem of remembering how many tokens were inside the container arose. To solve this problem, the Mesopotamians started impressing pictures of the clay tokens on the surface of the clay container with a stylus. Also, if there were five clay tokens inside, they would impress the picture of the token five times, and so problem of what and how many inside the container was solved.
Subsequently, the ancient Mesopotamians stopped using clay tokens altogether, and simply impressed the symbol of the clay tokens on wet clay surfaces. In addition to symbols derived from clay tokens, they also added other symbols that were more pictographic in nature, i.e. they resemble the natural object they represent. Moreover, instead of repeating the same picture over and over again to represent multiple objects of the same type, they used diferent kinds of small marks to "count" the number of objects, thus adding a system for enumerating objects to their incipient system of symbols. Examples of this early system represents some of the earliest texts found in the Sumerian cities of Uruk and Jamdat Nasr around 3300 BCE, such as the one below.
You can read more about the previous example at www.metmuseum.org.
The Sumerian writing system during the early periods was constantly in flux. The original direction of writing was from top to bottom, but for reasons unknown, it changed to left-to-right very early on (perhaps around 3000 BCE). This also affected the orientation of the signs by rotating all of them 90° counterclockwise. Another change in this early system involved the "style" of the signs. The early signs were more "linear" in that the strokes making up the signs were lines and curves. But starting after 3000 BCE these strokes started to evolve into wedges, thus changing the visual style of the signs from linear to "cuneiform".
By 2800 BCE the writing system started to exhibit use of phonetic elements. As the Sumerian language had a high number of monosyllabic words, there was a high degree of homophony, meaning that there is a large number of words that sound alike or identical. This presented the possibility of rebus writing, where sign for one word is used to represent another word that has a similar or identical sound. One example is ti "arrow", which is similar to til "life". So, to write "life", the ancient Sumerians wrote the sign for "arrow". Eventually, the logogram for "arrow" became a syllabogram to represent the sound /ti/. Similarly, other logograms also became syllabograms.
On the flip side, if different similar-sounding words all have different signs, then there could have been multiple ways of writing the same sound. This is the case with the syllable /gu/, as there are fourteen symbols that all represent the sound /gu/, of which four are shown below.
Note: When transcribing Sumerian syllabic signs into English, archaeologists use subscripts to mark different signs that have the same phonetic value. So in the previous example, gu is "flax", gu2 is "neck", gu3 is "voice", and so forth. And as you will see later, when transcribing logograms, capital letters are used, such as MUSHEN for "bird".
Another peculiarity of the writing system is polyphony, where many words that have similar meaning but vastly different sounds are written with the same sign. For example, the word zu "tooth", ka "mouth", and gu "voice" are all written with the sign for gu3 "voice".
In addition to use of phonetic signs to spell out new words, new signs were created by adding graphic elements to an existing sign or combining two existing signs. The additional graphic element could be geometric patterns without any meaning, or could be another cuneiform sign.
As the system grew more complex, it became hard to tell if a sign was being used as a logogram or a syllabogram (or even which one of the potential sound values the syllabogram can have). To help with the ambiguity, several logograms were overloaded to become "determinatives". They would precede or follow a group of signs that make up a word, and gives a hint to meaning of the word by marking the broad category of objects or ideas the word belongs to.
Note: When transcribing a determinative, archaeologists use small, superscript capital letters to write the Sumerian word that the determinative means, such as GISH for "wood".
Another way to disambiguate the reading of a sign is to use "phonetic complements" placed before or after (or both ways) a sign that gives part of the word's pronunciation. For example, the word uga means 'raven' in Sumerian, and there is a logogram UGA for 'raven'. However, the same logogram can also be NAGA ('soap'), ERESH (name of a city), or NISABA (the patron goddess of Eresh). To explicitly spell out the word uga, not one but two phonetic complements were used, one placed before the logogram and one after. And to top it off, they put the determinative for bird, MUSHEN, after the group of signs to make it absolutely clear that this is a raven.
Another interesting fact about Sumerian (and later cuneiform systems as well) is that the numeric system is both decimal (base-10) and sexagesimal (base-60). This means that there are unique symbols for each of the bases, as well as combinations and powers of the bases. So for example, the number nine would be represented by nine copies of the "1" sign, but the number ten would be represented only by the "10" sign. The number sixty would be represented only by the "60" sign, and the number seventy would be the "60" sign followed by the "10" sign.
The sexagesimal part of this system survives in the modern era in units of time (seconds and minutes) and of trigonometry (360 degrees).
Later Mesopotamian people (Babylonians, Assyrians, Persians, etc) adopted this system but modified it so that it became positional (like ours). This reduced the system to only two symbols (the "1" and "10" signs) and the position a sign occur within a number changes its quanity, just like "1" in the number "100" is different from the "1" in the number "10,000" in our modern system.
The Sumerian writing system was adopted and modified by other contemporaneous Mesopotamian people such as the Akkadians and the Babylonians. As a spoken language, Sumerian died out around the 18th century BCE, but continued as a "learned" written language (much like Latin was during the Middle Ages in Europe). In this way, Sumerian was used continually until the 1st century CE, making it one of the longest used writing system in history.