You have an interesting follis from the ancient Roman Empire. It is made of a thick core of bronze covered with a thin wash of silver, and bears Emperor Constantine's likeness (CONSTANTINVS) on the front and the Roman god Mars (MARTIS) on the back. Mars is dressed in full military attire and holds a spear and a shield.
It is pretty neat, I think, that you can hold such a piece of antiquity in your hand. Amazing!
Both the obverse and reverse designs stay roughly the same. The bust type of Constantine is what varies the most: mostly he's looking to the right, but sometimes he's looking left. Mostly he's wearing a laureate wreath, but sometimes he's helmeted and holding a spear. The reverse with Mars almost always has him walking towards the right, but on a few types he walks towards the left.
The obverse and reverse legends both vary quite a bit. The obverse will always contain the emperor's name, but the titles around it can vary a bit. A couple examples are 'FL VAL CONSTANTINVS NOB C' and 'IMP CONSTANTINVS PF AVG'. As for the reverse legends, 'MARTI CONSERVATORI' is the most common type, but there are others such as 'MARTI PATRI CONSERVATORI', 'MARTI PATRI PROPVGNATORI', as well as different abbreviations of these.
Below Mars' feet on the reverse are a few letters denoting the mint. This is known as the 'exergue' and is a valuable tool to find out where the coin was struck.
Typical values for these coins run as follows:
MOST COMMON TYPES:
worn: $5 US dollars approximate catalog value
average circulated: $20
well preserved: $80
Coins with Mars walking left or Constantine looking left are less common - multiply above values by 2.
Coins with 'P ARL', 'T ARL, or 'Q ARL' in the exergue were struck and Arles and are uncommon - multiply above values by 4.
Coins with this design, but the reverse legend of 'MARS VICTOR' or 'MARTI PACIF' are ancient error coins - multiply above values by 8.
Coins where the emperor is looking left, wearing a high-crested helmet and holding a spear are rare - multiply above values by 10.
Coins with the letters MOSTT in the exergue were struck at the Ostia mint and are very rare - multiply above values by 15.
There are hundreds of types of these coins, based on the variations of letters in the exergue, the reverse fields, the emperor's portrait, the obverse inscription, the reverse inscription, the way Mars is standing, and much more. To fully explore this series and find out which types are common and low-value, and which types are rare and valuable, you need a coin catalog. For the Mars folles of Constantine, you would need two: Roman Imperial Coinage Volume VI for the earlier coins before 313 AD, and Volume VII for the later coins after 313 AD.
Of course with ancient coins like this one, prices vary widely with the overall appeal of the coin. Coins that look like our picture are highly desired because they look nice, have even color without corrosion, and the pattern and inscriptions are easily readable. Such coins would usually sell around $100 retail price to collectors. If you were asking a coin dealer to buy it from you, a reasonable offer would be $50 or so. The dealer needs the mark-up to keep the dealership solvent.