In the fall of 1888, a person, who, at the time nicknamed "Leather Apron" was terrorizing the Whitechapel district of London. The Ripper only targeted prostitutes, and killed them in needlessly ferocious ways.

From April 1888, to February 1891, the Whitechapel district of London saw 11 total murders get committed. These murders were known as 'the Whitechapel murders'. Five of them are thought to be the work of a man nicknamed 'Jack the Ripper', or 'Leather Apron', as he was referred to back then. The Ripper only targeted prostitutes, and mutilated their bodies to varying degrees.

Mary Ann Nichols' body was found on Buck's Row, on the pavement, at approximately 03:40 in the morning on August 31, 1888 by Charles Cross and Robert Paul. Nichols had been 43 years old at the time of her death, and had been working as a prostitute. When she was found by Cross and Paul, she had, according to Paul, still been breathing, while Cross insisted that that had not been the case. However, neither of the men called for help, but instead hoped to come across an officer while on their way to work.
Neither of the men wanted to be late for work. (Kinda strange if you ask me.)

Annie Eliza Chapman's body was found in the backyard of 29 Hanbury Street, somewhere between 05:30 and 05:50 in the morning on September 8, 1888. The woman's body was found by a man named John Davis. Upon arriving on the scene, officers were met with a gruesome site: "The body was terribly mutilated." (stated by Dr. George Phillips, the doctor who arrived at the scene, on September 13.)
At around 05:20, a man by the name of Albert Cadosch had been in the backyard of neighboring 27 Hanbury Street, when he heard some commotion coming from nearby. According to Cadosch, the commotion consisted of "barely audible" voices, with the only word Cadosch being the word "No!", as well as something falling against the fence a short while later.
Roughly ten minutes later, a woman named Elizabeth Long spots a man and a woman conversing outside 29 Hanbury Street. According to Long, the man had his back towards her, while she was positive the woman was Chapman. Chapman's death was presumed to be just moments later.
It is possible that either Cadosch or Long got the time wrong, and that could mean that Cadosch was a witness to Chapman getting killed. Alternatively, the commotion Cadosch heard and the people Long saw had nothing to do with the killing.
Unfortunately, we will never know for certain.

The reason these two women are listed together is because both of them got killed on the same day (September 30, 1888), 900 meters away from each other, and only minutes apart. Stride only recieved a cut to her throat, while Eddowes had been disemboweled.

Elizabeth Stride

Stride was found by a man named Louis Diemschutz at approximately 01:00 in the morning. Diemschutz found Stride laying in Dutfield's Yard, a small space located at the side entrance to 40 Berner Street, a clubhouse that had been populated while Stride was killed. NOTE: There was only one entrance to Dutfield's Yard, and it was located next to the side entrance to 40 Berner Street. Stride had only recieved a minor cut to her throat.

Catherine Eddowes

Catherine eddowes was found by constable Edward Watkins in Mitre Square, while doing his regular patrols, at 01:44 in the morning. Watkins stated that his patrolling pace took him through Mitre Square toughly once every thirteen minutes. Indeed, just fourteen minutes prior, at 01:30, Mitre Square had been deserted. But now, at 01:44, it had been turned into a crime scene. Eddowes had been disemboweled, with Watkins stating that he "saw her throat was cut and her bowels protruding", that "The stomach was ripped up", and that the woman had been "lying in a pool of blood".

What is so strange about this incident is that both in Dutfield's Yard, and Mitre Square, there were people mere meters or even centimeters away, so why did no one hear anything?

Mary Jane Kelly's body was found in Miller's Court, Room 13, when a man named Thomas Bowyer had been sent out to check up on Room 13, at approximately 10:45 in the morning on November 9, 1888. Kelly had been in her mid-twenties at the time of her death, and had worked as a prostitute. Other than that, much of her identity remains a mystery to this very day.
Kelly's body was so badly mutilated that constable John McCarthy described it as looking "more like the work of a devil than of a man". There was a fireplace inside Room 13, and a few scraps of cloth were found in and around it. It is unclear wether the fireplace was used to destroy evidence or not.

The circumstances in which the women were found in were all similar: Killed hours, or even minutes before anyone arrived, and mutilated extensively, even having entire organs, mostly the uteri, removed. The last point will become more important in just a second.

All of the women mentioned above were killed either on weekends, or on holidays, which might tell us that the Ripper had a full-time job. Judging by how mutilated each of the womens' bodies were, I'll also assume that the Ripper absolutely did not like prositutes, if not women generally, although I can't be sure.

I'll also mention the conflict between the group of people who say the Ripper made the cuts and incisions "professionally", like a physician, or a butcher, and the group of people who say the exact opposite, that being that the Ripper made the cuts and incisions crudely, like someone with no experience. Here, I have nothing to say because I wasn't there when the killings took place. :/

The most likely candidate I found who mostly fit all of the criteria is "Dr." Francis Tumblety, a self-proclaimed medical professional, who specialized in herb-based medicine. In reality, however, he was nothing more than a fraud, or, more commonly known in the medical industry, a quack. In short, he was actually not a medical professional, but someone who likely wanted to make a quick buck scamming people.
This may not seem incriminating, and it isn't. However, the next point is. Tumblety had a collection of uteri he kept. These uteri came from "every class of women"(I don't know where the quote comes from, but the statement is stated as a quote everywhere I could find, and thus I will state it as a quote too.).
To add fuel to the fire, I'll also drop the fact that Tumblety was a misogynist, due to a failed marriage to, guess what: A prostitute. Because of these two key reasons, I am convinced that Tumblety was, in fact, Jack the Ripper. Of course, until further evidence pops up (which is unlikely), I can't actually accuse him.

However, I will say this: The mocking tone of the letters (shown below) is something I think matches Tumblety, as I believe that he actually did talk in a way that was mean in some way. Furthermore, many witnesses who saw the women before they died sometime stated that they (the women) were with a "well-dressed man".

Going by the image shown on Tumblety's Wikipedia article, I'd say that we have ourselves quite the suspect.

The letters play quite a significant role in this investigation.
They are perhaps one the most important pieces in it.
The letters are a controversial area in the investigation, due to no one knowing wether any of them are real. Professional and personal (so, mine) analyses suggest that the first three were likely written by the same person. What also suggests that they were real is that one of them, which also had very similar handwriting, was sent alongside a portion of a medically confirmed to-be human kidney, which was preserved in wine.

Dear Boss,
I keep on hearing the police have caught me but they wont fix me just yet. I have laughed when they look so clever and talk about being on the right track. That joke about Leather Apron gave me real fits. I am down on whores and I shant quit ripping them till I do get buckled. Grand work the last job was. I gave the lady no time to squeal. How can they catch me now. I love my work and want to start again. You will soon hear of me with my funny little games. I saved some of the proper red stuff in a ginger beer bottle over the last job to write with but it went thick like glue and I cant use it. Red ink is fit enough I hope ha. ha. The next job I do I shall clip the ladys ears off and send to the police officers just for jolly wouldn't you. Keep this letter back till I do a bit more work, then give it out straight. My knife's so nice and sharp I want to get to work right away if I get a chance. Good Luck.

Yours truly Jack the Ripper

Dont mind me giving the trade name

PS Wasnt good enough to post this before I got all the red ink off my hands curse it No luck yet. They say I'm a doctor now. ha ha

I was not codding dear old Boss when I gave you the tip, you'll hear about Saucy Jacky's work tomorrow double event this time number one squealed a bit couldn't finish straight off. ha not the time to get ears for police. thanks for keeping last letter back till I got to work again.

Jack the Ripper

From hell.
Mr Lusk,
Sor
I send you half the Kidne I took from one woman and prasarved it for you tother piece I fried and ate it was very nise. I may send you the bloody knif that took it out if you only wate a whil longer

signed
Catch me when you can Mishter Lusk

There are, of course, other suspects that I won't list here. One source for them is on Wikipedia.
There are also other letters found on casebook.org. I did not list them here, as I, like most others, believe that the ones I just listed are the only real ones, while the rest are fake.