Saiyans can learn multiple languages due to they're profession which commonly mercenary work.

Your Physical Abilities, STR, DEX, WIS, and CON increase by 1.

Saiyans have 5 special forms that almost any of them can learn. Super Saiyan, Super Saiyan 2, Super Saiyan 3, Super Saiyan God, and Super Saiyan Blue.

Super Saiyan: At 6th level, this form can be used three times a day for as long as you want, until turned off or until you take 1/4th of your max health in damage in one attack or in general. This gives a walking speed of 35, a +20 to your flying speed , and you have a +7 bonus to attack and damage rolls. You can't activate this again without first having a long rest.

Super Saiyan 2: At 13th level, this form can be used three times a day for 2 hours, or until you take 1/4th of your max health in damage in one attack or in general. Your walking speed becomes 40, and a +30 to your flying speed . You have a +1 bonus to attack and +14 to damage rolls. You gain 10 Temporary hit points. You can't activate this again without first having a long rest.

Super Saiyan 3: At 17th level, this form  can be used three times a day for 3 hours, or until you take 1/4th of your max health in damage in one attack or in general. Your walking speed becomes 50, and a +40 to your flying speed . You have a +2 bonus to attack and +21 to damage rolls. You gain 20 temporary hit points. Your AC raises by 1 in this form. You can't activate this again without first having a long rest.

 Super Saiyan God: At 19th level, this form can be used two times  a day for 25 minutes, or until you take a 1/4th of your max health in damage in one attack or in general. Your walking speed becomes 100, and a +60 to your flying speed . You have a +2 bonus to attack and + 30 to damage rolls. You gain 50 temporary hit points. Your STR, DEX, and CON scores become 19 in this form if they aren't  already.With this form you now have acquired divine ki this kind of ki allows you to be no long detectable by mortals who cannot use divine ki. You can't activate this again without first having a long rest.

Super Saiyan Blue: At 20th level, this form can be used three times a day for as long as you want, until turned off or until you take 1/4th of your max health in damage in one attack or in general. Your walking speed becomes 120, and a +90 to your flying speed . You have a +2 bonus to attack and + 70 to damage rolls. You gain 80 temporary hit points. Your STR, DEX, and CON scores become 20 in this form if they aren't  already. Also your ki can no long be detected by mortals who cannot use divine ki. This form is basically a Super Saiyan God gone super saiyan. You can't activate this again without first having a long rest.

During a full moon or when large amounts of blutz waves are present, and you have a tail, you transform into a Great Ape. This form is controlled by the DM unless you are 5th level. During the transformation the size of your saiyan increases dramatically, you become covered in thick brown or black fur,  gaining an elongated snout, your teeth becoming razor-sharp, your feet turn it hands, and your eyes becoming solid red.  Your alignment shifts to chaotic neutral until you are 5th level.Walking speed becomes 20, and you have a +1 bonus to attack and damage rolls. You can only use unarmed strikes that do 1d10 + strength modifier in damage. You gain 10 temporary hit points. Your size becomes gargantuan.

 So of the abilities you'll have are:

Breath Blast: A Great Ape can fire a Ki blast from their mouth that's a 100-foot line of destructive force/fire damage, on impact with any surface it deals 2d8 damage per level of the character up to level 12. Characters in the affected area can make a DEX saving throw. On a success the take half damage. Recharge time is 1d4 rounds.

Improved Grip: As an action, the Great Ape can grapple an opponent and use Crush as a bonus action dealing 4d6 force damage.

Boulder Toss: Great Apes can try to break off a chunk of land or pick up any large object that weighs up to 500 pounds and hurl it at an opponent or object. The range is 120 feet. The thrown boulder deals 3d6 damage to anything within 10 feet of the impact square. DC 15 DEX saving throw, on a success they take half damage.

Objects may be carried and manipulated with it, including fine manipulations. You cannot hold a weapon or shield using your tail. Due to the increased balance your tail grants you, you are proficient in the Acrobatics skill. If your tail is severed, you are no longer considered proficient in Acrobatics unless your class deems otherwise. If your was cut off or removed in any other way tail, you can grow one if you want to in 1d4 days. Also roll 1-d2 (flip a coin) to see if your tail will even grow back at all. If the regrown tail gets cut off again it will not be able to grow back.

When you become unconscious, by getting down to 0 hit points, after being brought back to consciousness you have a permanent boost to your STR and DEX by +2. This doesn't apply if you die and are then revived. This does apply if you are brought to 0 hit points and healed.

Your size is medium. 

Your walking speed is 30.

Saiyans have learned how to fly due to the mastery over their ki. Your flying speed is 50. 

Saiyans live to be a century old at average, and mature at 18. They don't start showing signs old age until their 80's.

Saiyans can sense the ki of any living creature within a 20ft radius of their surroundings. At 6th level, they can tell if the creatures have good or evil ki.

Saiyans can also raise and suppress their ki. Their ki will usually raises when they transform, especially during the super saiyan transformation.