Futo Inu:
Your rifle is almost certainly what is called a M96/38b.
It probably has a straight bolt, is stamped Carl Gustaf on the reciever above the date and has a threaded barrel end for accepting a blank cartidge adaptor.
The M96 rifles were made at the Swedish Carl Gustaf works (475,000 rifles) from 1899 to 1925 and a Waffen Fabrik Mauser Obendorf (40,000 rifles) in 1899 and 1900.
If your rifle is dated 1913, it probably has a nice walnut stock. They switched over to beech (mostly) between 1914 and 1916 when their stores of walnut ran out during WWI. Apparently, they do not have a lot of walnut in Sweden. I like the old walnut stocks best of all, so this is nice.
In 1925, the world looked very peaceful, so the Swedes stopped making these rifles.
By the late thirties, it was obious that war was again immanent. Since long 29" barrels had gone out of style, some 30,000 M96 rifles were converted to to a new 24" barrel configuration by Carl Gustaf between 1938 and 1940. These are the M96/38b's, of which yours is probably one.
Finally, they decided that they did not have enough rifles, so they made another 20,000 thousand M96 rifles and 60,000 M38 rifles between 1942 and 1944, but all of these were made at the Husqvarna works. The M38's had bent bolts and 24" barrels. If yours was one of these, it whould have Husqvarna stamped on the reciever.
The Swedes were very good at keeping all the proper serial numbered parts together. You will see matching serial numbers all over you rifle, probably even the stock and hand guard if you take the action out of the stock and look in the barrel channel. The reason for this is that all these parts, though machine made, were carefully hand fitted together while in the white before final finishing and heat treatment for a near perfect fit. The parts so fitted then all had to come back together after final finishing to the same rifle. The Swedes were vey proud of their craftsmanship and rarely mismatched any parts unless it was absolutely necessay, even when they converted the M96 to the M96/38.
If your barrel has the full serial # on it, it is the original barrel. If it has only the last three digits, it is a replacement barrel. I would guess if it is 1913 and in top shape, it is a replacement, which is good if you like to shoot.
The Swedish Mausers are realy great rifles. The only thing I would criticize is the straight grip stock, which nearly everyone else abandoned for a pistol grip even bere WWI and that danged threaded barrel end. Whoever thought that one up certainly had no eye for nice looking rifles.