Define Ilm Al Hadith (Science of Hadith)
Ilm al hadith means Science of Hadith, which refers to the Knowledge of the scrutiny of hadith literature. Basically every hadith has a chain (isnad) of narrators that are going all the way back to the Prophet ﷺ. Studying biography of each narrator in a chain who transmits the hadith, in addition to comparing it with other chains of that same hadith, if any, including studying linguists of text as well as circumstances involved when particular hadith was narrated and others factors involved in recording are all included in the subject of ilm al hadith. There exists a few common misconceptions that the collection of hadith took place many years, in most cases 200 years, after the Prophet's death or that its initial collection was started by the students of the companions, and Prophet Muhammad ﷺ and his companions never supported or indulged in this activity. Such misconceptions are false because there is evidence that hadith were being collected during the Prophet's life (discussed in subsequent posts) and in fact the foundation and practice of Ilm Al hadith (Science of Hadith) was initiated by his companions, in a more organized manner especially during the rule of Umar ibn Khattab (r.a), the 2nd successor of Prophet Muhammad ﷺ.
Foundation of Ilm Al Hadith (Science of Hadith)
Umar (r.a) was the first to realize the necessity of the proper sifting of the hadith narrations. Those who narrated any hadith were required to produce some witnesses in support of the tradition. In this way a rich corpus of Hadith was built up. Umar (r.a) classified the traditions in two broad categories. One category of traditions pertained to religious, moral and social affairs pertaining to the community at large. The other traditions revolved round the person of the Holy Prophet ﷺ and pertained to his words and deeds as a human being i.e. the Prophet's Sunnah. Umar (r.a) distinguished between these two categories. All matters falling in the first category were binding and had the status of law. Umar (r.a) evolved the following principles on the basis of which the traditions were to be accepted:
(1) The report should be literally faithful;
(2) Every Hadith narrated should carry with it the name of the narrator and the chain of narrators;
(3) The narrators must be men of proven faith and integrity;
(4) In judging the veracity of a report the occasion and circumstances involved should be taken into consideration;
(5) The report should not be repugnant to the Holy Quran;
(6) The report should be rational.
Subsequent Developments in Ilm Al hadith (Science of Hadith)
By the end of 1st century Hijrah (100 AH - 720 CE) majority Companions passed away leaving their compilations behind including the framework and process for hadith evaluation taught to Tabi’een (their students). However this process needed to be a bit more supervised especially to avoid and separate the unauthentic traditions that began circulation in subsequent years. Therefore, during the rule of Umar bin Abdul Aziz (r.a) (717 - 720 CE), one of the Ummayad Caliphs (also known as 2nd Umar due to his piety), ordered the collection of ahadith on a large scale. He assigned learned scholars and hadith experts of Madinah such as Abu Bakr Ibn Hazam (Qadi of Madinah) and famous Ibn Shihab al-Zuhri, who were also students of Prophet's companions, Ayesha (r.a) and Anas bin Malik (r.a), expert hadith specialists and teachers. During the mid of 2nd century Hijrah (150 AH), hadith centers came to exist and scholars like Imam Malik (Died 179 AH) and Sufyan Thauri (Died - 168 AH) and several others opened their centers to teach hadith with rules as laid down by their predecessors.
In subsequent years rules of hadith collection were expanded and further conditions were added such as ilm al rijal (names of narrators and their biographies) and each hadith that included a chain (isnad) of narrators was classified based on the reliability of the narrators such as their piety, intelligence, if they were of forgetful nature, or if they were known to ever have lied. It was based on the strength of the narrators is how each hadith came to be classified with a status such as Dhaeef (weak), Sahih (authentic), Mutawattur (narrated through several chains), Hassan (good - lesser than Sahih), Ghareeb (strange due to some interruption in chain). Based on each status later compilations were made such as Sahih Bukhari and Sahih Muslim, with sahih meaning they are very authentic due to evaluation involved in their chains. One of the authors of Hadith book comments on this unique process: “Every Muhaddith (hadith expert) even today, when describes a hadith, he suffixes it with a specific name of a hadith denoting its level of authenticity (such as ‘Hassan’ or ‘Sahih’), then quotes the book of hadith where its documented (such as Musnad of Ahmad) and then prefixes it with an unbroken chain of narrators spreading over the last 1400 years through whom he received the hadith. No other religion, nation, party or even small group of people can show the parallel of what early Muslims did to ensure the authenticity of hadith and Sunnah.”
In subsequent centuries scholars studied these ahadith, added their comments to explanations given by their teachers and developed upon the wisdom and knowledge, resulting in science of Fiqh (practices/ruling) & Shariah (Islamic law). It is extremely sad to see that today many Muslims doubt the authenticity process of all hadith or some of it, without researching. And worst is that some even compare the uniquely systematic collection of this literature with collection of Christian Gospels that clearly lacked any consistent methodology and process in its compilation.
 Masud-ul-Hasan, Professor. 1982. "Khalifa bin al-Khattab - Hadith and Fiqh." Alim - The world's most useful Islamic software. Accessed 03 05, 2019. http://www.alim.org/library/biography/khalifa/content/KUM/16/1 . (Masud-ul-Hasan 1982)
 Kazi, Mazhar. April 1, 2007. Guidance from Hadith & Sunnah. Al-Huda Publications - (Kazi April 1, 2007)