This would be the first Man-Kzin war (The Kzin are a creation of Larry Niven and first seen in his book Ringworld.
First Man-Kzin War
The Kzinti, with vast technical superiority (including gravity drives, telepaths, and a large military empire), detected a human colonization ship in deep space, the Angel's Pencil. After the Kzin telepath learned that the humans were unarmed and didn't even understand the concept of weapons, they attempted to kill the human crew in a slow, painful manner using an inductive heating weapon hoping to capture their ship intact for intelligence purposes. However, one of the humans used the ship's powerful drive system (which doubled as interstellar communications laser) as a weapon and destroyed the Kzin ship, beginning the First Man-Kzin War. The crew then warned Earth of the warlike aliens, although the transmissions were initially dismissed as an outbreak of psychosis. Then a similar encounter between another human ship and Kzin vessel led to the destruction of the more primitive human ship. However, one of the human prisoners, with the aid of a rogue telepath, was able to escape to the Angel's Pencil and warn them of the danger from their increasing penetration into Kzinti space.
In the course of the First Man-Kzin War, the Kzinti invaded and occupied the human colony of Wunderland, in the Alpha Centauri system, as a staging point for an attack on Earth. Human ships attempting escape back to Earth were shot down, but a single vessel managed to carry some refugees to the sister colony We Made It. The Kzinti fleet moved on to Earth, but in a replay of first contact, the peaceful humans used laser communications, fusion drives, and mass drivers to cut the first invasion fleet to ribbons. Over the next several decades, three more fleets were launched against Earth, and all were beaten back. However, after near defeat by the fourth fleet, it was becoming clear to Earth's military leaders that the Kzinti were learning to wage war more effectively than their traditional "scream and leap" tactics, and that the Solar system's defenses would quickly succumb to the Kzinti's superior numbers, firepower, and technology, were it only wielded with a modicum of tactical and strategic sense. In order to delay the next attack, a Terran Bussard ramjet starship was utilized to transport and deploy several relativistic kill vehicles in the Wunderland system. Using iron slugs accelerated to 99% of the speed of light, it devastated a portion of the planet, killing humans and Kzinti alike and delaying the launch of yet another Kzin fleet against Earth. A number of specialists traveled aboard this ship, using Slaver stasis fields for lithobraking, and successfully assassinated the Kzin military leader on Wunderland, Chuut-Riit. Despite this setback for the Kzin cause, preparations for a fifth and decisive assault fleet were nearing completion.
At this point, a passing Outsider ship sold the colony of We Made It the manual for a hyperdrive, a technology unknown to the Kzinti. Dimity Carmody, an escapee from Wunderland and a genius who had toyed with FTL drive concepts since before the occupation, managed to construct a working prototype drive using the manual. Hyperdrive ships were dispatched to Earth, where the faster-than-light drive was installed on several ships for a preemptive attack on the Fifth Invasion fleet. The attack hit the Kzin amidst internal struggles following the death of their leader. Due to the huge success, Wunderland was quickly liberated, freeing the fleet to attack other Kzinti worlds. The FTL drive allowed the human fleets to coordinate and concentrate their forces beyond anything the Kzinti could manage, even letting them outrun and jam the news of each successive Kzin defeat. The first indication the Kzinti Patriarchy had, that much of the Kzin empire was gone and that a significant percentage of all Kzinti had died was when human warships appeared in the skies above their homeworld.
Meanwhile, however, on Wunderland, now liberated by humans, several surviving Kzin, led by Vaemar-Riit, last surviving kitten of Chuut-Riit, and with the cooperation of Dimity Carmody, Nils Rykermann, Leonie Rykermann and other humans, began to cautiously cooperate with humans and try to learn human ways. Vaemar-Riit even enrolled at a human university and obtaining a reserve officer's commission. These became known as the Wunderkzin, and some later proved to be human allies. This slowly growing Man-Kzin co-operation was bitterly opposed both by many other Kzin and by many revanchist humans on Wunderland, while others among the human and kzin communities on Wunderland sought to manipulate the situation for their own ends. There were also ongoing human situations - for example Nils Rykermann, a Wunderland academic, in love with Dimity Carmody, married Leonie Rykermann, one of his students, during the occupation, believing Dimity to be dead. This situation has not been resolved. There was also a somewhat ambiguous growing relationship between Dimity and Vaemar-Riit; the two are depicted together on the cover of Man-Kzin Wars XI.
The war ends in 2433 with the signing of the MacDonald-Rishaii Peace Treaty. The vast majority of the Man-Kzin Wars stories are set around the First War.