In old music works Gamakam is defined as shaking of the note. But even sliding from note to note (Jaaaru) is included in the list of Gamakams in Sangeetha Sampradaaya Pradarsini of Subbarama Deekshithar (1905). English versiona of the 4 volumes of Sangeetha Sampradaya Pradarsinni are available here He had developed symbols to represent different Gamakams (14 in number) and his notations include these symbols.. But this effort has not been widely followed. Most of the notation published do not give any indication about Gamakam, except for an occasional wavy line. In teaching also, rarely names of Gamakams are mentioned, except sometimes in teaching Veena. By and large the student learns the Gamakams by listening to the teacher's rendering. You can skip the descriptions of names of Gamakams, but listen to them to see the varieities
The most common Gamakam is 'Kampitham' which is the oscillation of a note. The oscillation could be very short in range as in Ga in Kalyaani Raagam. (Only this type of gamakam is treated as Kampitham in Sampradaaya Pradarsini). In many cases the lower note (or an intermediate position) is used as the anchor and note is oscillated up to its own position or over a range of 1, 2 or even 3 notes (such oscillaions touching other notes are called 'Vali' in Sampradaaya Pradarsini). Oscillations spanning 2 notes are common for ri1, ga2, ma2, da1 and ni2. In the case of ma2 the upper note pa is usually the anchor. For ri1 and da1 usually only short range Kampitham spanning 2 notes is used. Listen to ri of Gowla (the phrase is 'sa ree'). Notes ga2 and ni2 may use both short and large range kampitham. Listen to ga of Kaanada using large range kampitham (the phrase is 'ri-gaa ma ri'. Kampitham may also be anchored on the higher pitch and oscillate downwards as in the case of ni of Surati.
'Nokku' or 'Thirupam' involves pulling of the Veena string even while the note is reached thus touching the higher note first before coming to the actual note. This could be in the ascent as in the case of on ga of Maayaamaalavagowla in the phrase 'sa-ri-ga'and ma is touched before ga is reached and on da & ni of Sankaraabharanam in the phrase pa-da-ni-Sa (ni touched before da and Sa touched before ni). This gamakam also occurs in the starting note of many ascending phrase such as ri of Sankarabharanam, ga1 of Aanandabhairavi in 'ga ma pa'. It is also used while turning on the note as in 'pa ma pa' of Bhairavi (the audio is 'pa ma pa da ni Saa'), ma being pulled from ga3 fret on Veena. It is an extensively used gamakam - as common as Kampitham
'Jaaru' is smooth slide from one note to another. When it is an ascending slide it is 'Etra Jaaru' and when descending it is 'Erakku Jaaru'. In fact there is always continuity between notes in any single phrase (which is the characteristic of Carnatic Music), but the term Jaaru is used when the slide pronounced and slower than usual ascent or descent between notes.