This post is a paraphrased translation (not an actual and complete translation) mixed with my own supplementary notes, of Chapter 1 of the book Fawaid al-Rijaliyah by Syed Ali al-Hussaini al-Sadr. The author in this book discusses various benefits of Ilm al-Rijal and its importance, and brings 40 benefits all together Those not familiar with certain Arabic ahadith terminology will not be able to understand the post completely. Please refer to my post How to Better Understand & Study Hadith for more information on the subject.

Chapter 1: Introduction to Ilm ul-Rijal
Definition: It is a science in which the states and conditions of the narrators are researched, and the qualities that they possess, which would cause us to accept their narrations or reject them. This includes, their trustworthiness, truthfulness, condemnation that they have been given or praise that they have been given and also whether they were prone to making mistakes or not.
Subject of Discussion: The narrators of the narrations of the Prophet & Imams are the subject of discussion. What is famous amongst the scholars is that their conditions (qualities) are discussed and researched.
Initiator of the Science: The first person to compile a book on Ilm al-Rijal was Abdullah bin Abi Rafi’ the freedman of the Prophet (pbuh) and the scribe of Imam Ali (as). He wrote a book titled: تسمية من شهد مع أمير المؤمنين. Some scholars have named him as Ubaydullah, and he was one of the special companions of Imam Ali. His progeny was one of the highest and best of companions of the later Imams as well. Aqa Buzurg Tehrani writes[1]:

كاتب أمير المؤمنين (ع) . له كتاب «قضايا أمير المؤمنين» و كتاب «تسمية من شهد مع أمير المؤمنين ع» الجمل و الصفين و النهروان من أصحاب رسول اللّه (ص) ذكره الشيخ فى «الفهرست» و ذكر أسناده فى روايته الكتاب عن عبيد اللّه المذكور. أقول هو أول من دوّن أسماء الرجال لأنه كان فى عصر أمير المؤمنين (ع) و كان كاتبه. و أبوه أبو رافع شهد حروب أمير المؤمنين كلّها. و اقتصر من ترجمة الرجال و تسميتهم على خصوص الصحابة، و اقتصر من بينهم على خصوص من شهد منهم حروب أمير المؤمنين (ع) لغرض اتمام الحجة على بعض الضعفاء و الجاهلين لحقيقة الأمير، بأنه لو قصروا عن مشاهدة دلائل حقيقته، لينظروا الى من تابعه و شايعه، و أفدى بنفسه فى نصرته و حمايته، ممن لا ريب فيهم. و هذا هو الجدال بالأحسن مع من كان فى ذلك العصر من المخالفين، كما قاله امام القراء و المفسرين أبو سعيد أبان بن تغلب، فقد روى النجاشى فى ترجمته، باسناده الى عبد الرحمن بن الحجاج، قال كنّا فى مجلس أبان بن تغلب، فجائه شاب، قال يا ابا سعيد أخبرنى كم شهد مع على بن أبى طالب (ع) من أصحاب النبى (ص) قال فقال أبان له؛ كأنك تريد أن تعرف فضل على ممن تبعه من أصحاب رسول اللّه (ص) قال فقال الرجل هو ذاك! فقال: و اللّه ما عرفنا فضلهم الا باتباعهم اياه، الحديث

After him, Abdullah bin Jaballah al-Kinani wrote a book as Syed Hasan Sadr claims in Ta’sees al-Shi’a li-uloom al-Islam [page 233]. Some have considered him to be one of the companions of Imam Kadhim (as). After him, came the works of Ibn Faddhal and Ibn Mahbub in the 2nd century-beginning of 3rd century Hijri. After that, the works become numerous and Aqa Tehrani claims that the books numbered in almost 500.
Benefit: One can determine the ‘adalah, trustworthiness, or goodness of a narrator through this science. Subsequently, the sanad (chain of narration) will become hujjah (binding proof) upon us. Once the sanad becomes hujjah, then the khabar (narration) can also become hujjah. Just like a khabar becomes hujjah when one reaches itminan of it being said by the Imam (itminan in its sudoor). Since the source of much of religious knowledge is through ahadith, we realize the important and benefit of this science as it helps us determine whether a hadith is hujjah upon us or not.
The Qur’an is more concerned with relaying the principles, whereas consensus (ijma’) is the uncovering of the opinion of a community upon which the Imam also agreed upon and therefore it is rarely a hujjah. Furthermore, intellect (aql) cannot arrive at all the rules by which we must abide by and therefore we must refer to the narrations.
It is known that not all the narrations have hujjiyah with regards to having been originated from the Imams and neither are they all Mutawatir in terms of their Sanad. In fact many scholars have said (including Ibn Taymiyah) that tawatur is personal and Urfi – meaning, it is a large number that brings itminan or even yaqeen for a person or a community. Since, most of the ahkam are khabar ul-wahid (solitary report), we are left with no choice but to prove its hujjiyah through examining the narrators in its sanad.
Therefore, there are two ways for a Khabar (report) to become Hujjah: 1) by analyzing the narrators of its sanad solely [the opinion of Ayatullah Khoei], and 2) or through other means  we reach itminan that this narration was indeed said by an Imam [one of the ways could be the first way]. In both methods, the need of Ilm ul-Rijal is there regardless.
A jurist must therefore, exhaust all his efforts in order to determine whether a narration is hujjah or not.
[1] مصفی المقال في مصنفي علم الرجال http://www.noorlib.ir/View/fa/Book/BookView/Text/19819/2/258