Categories of hadeeth
Question

I would like to understand the categories of hadeeth. For example, what is meant by a “ghareeb hasan” hadeeth? What are the hadeeths that it is permissible to take as evidence?
Praise be to Allah.Firstly: 
We praise Allah for guiding you to ask about this and try to understand the terminology of the hadeeth scholars and the meaning thereof, because this is great and noble knowledge which the scholars devoted their lives to understanding and explaining. Nevertheless, every Muslim who is keen to acquire sufficient education in this field of knowledge may do so, in order to understand what he reads sometimes on Islamic webpages, and so that he will be able to build his knowledge on a solid foundation after that. 
Hence our advice to you is to read a brief discussion on the science of mustalah al-hadeeth (the science of hadeeth), in which you will find all that you need to know about the hadeeth sciences and terminology used by hadeeth scholars. One of the books we encourage you to read is the commentary by Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) on the book al-Manzoomah al-Bayqooniyyah, which you can find on the following link (in Arabic):
http://www.islamway.com/?iw_s=Scholar&iw_a=series&series_id=1367
Secondly: 
With regard to the categories of hadeeth, the scholars have various ways of categorizing different types of hadeeth, in each of which they examined the hadeeth from a specific angle. 
When they looked at the issue of who the hadeeth was attributed to, they divided the hadeeth into the following categories: 
1. Marfoo‘: if the hadeeth was the words of the Prophet (blessings and peace of Allah be upon him)
2. Mawqoof: if the hadeeth was the words of the Sahaabi (may Allah be pleased with all the Sahaabah)
3. Maqtoo‘: if the hadeeth was the words of the Taabi‘i.
This categorization has been discussed previously in the answer to question no. 121290.
 When they looked at the isnaads of the hadeeth, which are the chains of narrators who transmitted the hadeeth from the one who spoke it, they divided the hadeeth into the following categories: 
1. Mutawaatir: if the hadeeth was narrated via many isnaads and narrations.
2. Ahaad (or ghareeb): if the hadeeth was narrated via only one isnaad and one narration; this was also called al-ghareeb al-mutlaq or al-fard al-mutlaq. But if the hadeeth was narrated by one Taabi‘i from one Sahaabi, then two or more narrators transmitted it from the Taabi‘i, this is called gharaabah nisbiyyah, i.e., it is ghareeb or aahaad with regard to the narration of that Taabi‘i from the Sahaabi.
When the hadeeth scholars looked at the ruling on the hadeeth, and whether it was to be accepted or rejected – and perhaps this is the main point of the question – they divided them into the following categories: 
1. Maqbool (accepted): if the hadeeth fulfilled the conditions of acceptability and was fit to be quoted as evidence and acted upon.
2. Mardood (rejected): if it did not fulfill the conditions of acceptability.
Then they divided the accepted hadeeths into a number of categories: 
1. Saheeh: if it fulfilled the highest conditions of acceptability. For more information, please see the answer to question no. 79163
2. Hasan: if it fulfilled the minimal conditions of acceptability.
In many cases the hadeeth scholars used other terms in addition to the terms mentioned above. For example, they sometimes call a hasan isnaad “jayyid”; sometimes they describe a saheeh hadeeth as “in accordance with the conditions of the two shaykhs (al-Bukhaari and Muslim)”; and other similar phrases. Although there are sometimes subtle differences between these terms, our aim in this answer is to make these categories easy to understand in general terms. 
The hadeeth scholars divided the rejected hadeeths into several categories: 
1. Da‘eef (weak): if it failed to meet any of the conditions of acceptability.
2. Mawdoo‘ (fabricated): if its isnaad includes anyone who was a liar or accused of lying.
In many cases, they also used other terms in addition to these. They sometimes described a da‘eef hadeeth as baatil (false), especially if it was extremely da‘eef; or they described its isnaad as taalif (worthless); or they described a mawdoo‘ hadeeth as makdhoob (a lie), and so on. For more information, please see the answer to question no. 6981. 
Thirdly: 
What is mentioned above refers to the terms mostly used by the hadeeth scholars in their discussions and their books. We have found that some scholars use more precise terminology, and they had some more precise criteria in describing the hadeeths, such as when Imam at-Tirmidhi (may Allah have mercy on him) says “a hasan ghareeb hadeeth.” 
When he says “a hasan hadeeth”, this indicates that the hadeeth fulfills the minimum conditions of acceptability, so it falls into the hasan category in terms of whether it is to be accepted or rejected. 
When he says “ghareeb”, this is a description of the hadeeth as being aahaad, although this does not rule out it having other isnaads. Hence what is meant is that this isnaad is being described as ghareeb. This is what is known as gharaabah nisbiyyah and not ghareeb mutlaq, which has no other isnaad. 
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said: 
When at-Tirmidhi says “hasan ghareeb”, it may be that it is ghareeb in this isnaad, but the matn (text) has corroborating evidence by virtue of which it classed as hasan. End quote. 
Majmoo‘ al-Fataawa, 18/24 
And Allah knows best.