| Often, the mints used to produce Roman coins were divided into several workshops that shared the duties of coin production. Studies of specific mints and specific rulers will show that the organization and number of these shops varied from time to time and place to place. Beginning in the mid third century AD, some coins bore marks indicating which shop or officina was responsible for its issue. The officina system was well developed long before the marks were first placed on coins. Students of earlier issues examine evidence of numbers of coins found in large hoards and the existence of die links to determine the mint structure for unmarked coins. This page shows coins issued with marks (taking all the work out of the matter?). After a few years of marking the workshops on coins, some issues also began to mark the mint city on the coins thereby inventing the mintmark as we usually use the term. It is interesting that the first use of open coding did not see fit to include the city information.
The first issue of openly marked officinae was from the Rome mint in 248 AD under Philip I. The reason for this addition (and the reason it was not adopted permanently at that time) is a matter of speculation. It is possible that some irregularities at the mint made it necessary to 'crack down' on the workers and require the signing of the dies. This issue shows six workshops numbered with Greek numerals in the reverse fields. Shops A, B, E and S (1, 2, 5 and 6) struck for Philip I while D (4) struck for Otacilia and G (3) for Philip II. Only one type was struck by each shop so, for example, all letter E marked coins are the two horsemen type shown above.
 
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At very nearly the same time the same six workshops issued the special coins for the millennium celebration. Again each of six workshops produced one type apiece and the same two (3 and 4) were used for Philip II and Otacilia. The difference is that the numbers here were Roman numerals placed in exergue. Or sample here is a Philip II from shop III (3). These 'special' SAECVLARES AVGG coins are seen much more frequently than the Greek numeral series but this may reflect the popularity of the animal types and link to the millennium celebration as much as their being more common. Following these two small issues, the mint reverted to the old practice of not marking the shops for the final issues of the reign. The same six shops produced six types for the remaining Philip issues but the coins were not marked. It would be most interesting to know why this numbering experiment was tried and why it was abandoned. The two series used the same six workshops but they were numbered once in Roman numerals and once in Greek. 'Why?' is never an easy question when working over 1700 years after the events.
Succeeding rulers ocasionally issued some coins marked by workshop but the practice did not become regular for some time. The Antioch mint of Trebonianus Gallus used an interesting mixture of Roman numerals and dots for some coins. The practice of using letters arose again under Gallienus and became more frequent with each year that passed. By the time of Probus, most mints were using some sort of officina numbering on the coins. Our example here shows the Serdica mint, 4th officina use of D following 
Other mints of the period used other ways of indicating the workshops. Lugdunum (left) placed a Roman numeral in exergue as had the Philip Saeculares issue. Ticinum (below) and some others used a series P, S, T, Q, V, and VI. For Primus, Secundus, Tertius, Quartius, Quintus, and Sextus. The problem of more than one ordinal beginning with the same initial was handled by using the Roman numeral for 5th and 6th. Our example below left shows the mark QXXT with the final T indicating the city Ticinum; Q is the officina mark: 4. An example of how it is necessary to examine more than one coin from a series to understand the system being used is offered by the coin below right. The mintmark TXXT has two different meanings of T. The first is the officina Tertius; second is the city Ticinum. Most cities used 
As inflation increased the demand for coins, the number of mints and shops had to be increased. Antioch under several emperors operated with nine officinae. These were numbered with the standard series of Greek numerals from 1 to 8 (A to H) but the 9th officina used ED
or 5+4 to avoid the unlucky numeral Q, first letter in the word Qanatos (death). These are no more scarce than the others the series but this collector finds the added interest of the additive officina mark worth a premium over the others. Am I crazy? Certainly, I collect. Usually, Antioch was divided into more shops than other mints. There was no direction from central authority requiring all mints be managed along the same lines. Each mint used an organization and markings as they saw fit leaving collectors a jumble of information needing to be set in order. 
By the time of Constantius II (c.350 AD) Antioch was up to 15 (EI) officinae and had left behind the fear of theta (perhaps due to Christianity??). The exergue of our ninth workshop example shows the city abbreviation ANT followed by Q. In the field is a large G, here indicating the issue and standard in this series of diminishing weight coins. Reading mintmarks on Roman coins is not a simple matter; they changed the rules whenever it suited the needs giving no thought to the troubles of coin collectors of later days. How do we know which letter serves which purpose? We must examine all of the coins possible and absorb their similarities and differences. Coin books are great references but there is no substitute for 'experiencing' a few thousand coins. 
This AE3 of Valens (364-378 AD) from the mint of Arelate (Arles) shows a very unusual mark of officina. It bears OF II in the reverse field. This carries the point of open marking one step further adding OF to indicate that the numeral is the officina rather than serving some other purpose. This idea did not catch on and later coins reverted to the more standard abbreviations. The city abbreviation in the exergue CONST (for Constantina, then the name of the city) is longer than often seen illustrating a move at this period to expand codes on coins. Perhaps 'truth in labeling' was fashionable for a few years in the fourth century.
As a footnote I want to show a coin of Septimius Severus from the Emesa mint. Dating to 194AD, a full 54 years earlier than the Philip that began this page, some examples from this series of coins show one or two dots following the reverse legend. What is the meaning of these dots? Are these early marks of workshop? I simply can not say for sure. This and thousands of other questions remain to be answered by numismatists of the future. Will we see this answer anytime soon? Is anyone capable of shedding light on this series going to be able to publish the answers to my thousands of questions? When you see a coin like this do you see questions or just another denarius of a common emperor? These are the questions that will decide if numismatics as a science has a future in the 21st century. I hope.