Steps leading to jhana/dhyana
There are 9 steps in concentration training leading to shamatha (pali samatha) as explained in Alan Wallace's "The Attention Revolution." What follows is a brief overivew of this map with 9 steps, 6 powers, and 4 types of engagements featured in Wallace's handbook, with additional notes on terminology from different sources (such as "Mahayanasutralankara" and "Shravakabhumi" by Maitreyanatha/Asanga,"Bhavanakrama" by Kamalashila etc.).

	Step	What is achieved	Power by which that is achieved	What problem persists	Attentional imbalances	Type of mental engagement	Quality of the experience	Involuntary thoughts
1	Directed attention	One is able to direct the attention to the chosen object	Learning the instructions (skt. shruti)	No attentional continuity on the object	Coarse excitation	Focused	Movement	Flow of involuntary thought like a cascading waterfall
2	Continuous att.	Attentional continuity to a chosen object up to a minute	Thinking about the practice (skt. asaya)	Most of the time attention is not on the object	Coarse excitation	Focused	Movement	Flow of involuntary thought like a cascading waterfall
3	Resurgent att.	Swift recovery of distracted attention, mostly on the object	Mindfulness (skt. smrti)	One still forgets the object entirely for brief periods	Coarse excitation	Interrupted	Movement	Flow of involuntary thought like a cascading waterfall
4	Close att.	One no longer completely forgets the chosen object	Mindfulness, which is now strong	Some degree of complacency concerning samadhi	Coarse laxity and medium excitation	Interrupted	Achievement	Involuntary thoughts like a river quickly flowing through a gorge
5	Tamed att.	One takes satisfaction in samadhi	Introspection (skt. samprajanya)	Some resistance to samadhi	Medium laxity and medium excitation	Interrupted	Achievement	Involuntary thoughts like a river quickly flowing through a gorge
6	Pacified att.	No resistance to training the attention	Introspection	Desire, depression, lethargy, and drowsiness	Medium laxity and subtle excitation	Interrupted	Achievement	Involuntary thoughts like a river slowly flowing through a valley
7	Fully pacified att.	Pacification of attachment, melancholy, and lethargy	Enthusiasm (skt. virya)	Subtle imbalances of attention, swiftly rectified	Subtle laxity and excitation	Interrupted	Familiarity	Involuntary thoughts like a river slowlyflowing through a valley
8	Single-pointed att.	Samadhi is long, sustained without any excitation or laxity	Mindfulness, introspection, enthusiasm	It still takes effort to ward off excitation and laxity	Latent impulses for subtle excitation and laxity	Uninterrupted	Stillness	Conceptually discursive mind is calm like an ocean with no waves
9	Attentional balance	Flawless samadhi is long, sustained effortlessly	Familiarity (skt. paricaya)	Attentional imbalances may recur infuture	Causes of those imbalances are still latent	Effortless	Perfection	Conceptually discursive mind is still like a great mountain

* Coarse excitation: attention completely disengages from the medit. object. Medium exc: involuntary thoughts occupy the center of attention, while the medit. object is displaced to periphery. Subtle exc: Medit. object remains at center of attention, but involuntary thoughts emerge at periphery of attention.
* Coarse laxity: Attention mostly disengages from medit. object due to insufficient vividness. Medium lax: Object appears, but not with much vividness. Subtle lax: Object appears vividly, but attention is slightly slack.

Terms for nine stages from Daniel Brown's "Pointing out the Great Way" (on the stages of meditation in the Mahamudra tradition) with Skt. original terms used by the Indian master Asanga:

1. Directing	cittasthapana
2. Continuously directing	(cittapravaha)samsthapana
3. Resetting	cittapratiharana / (citta)avasthapana
4. Staying closely	cittopasthapana
5. Disciplining	cittadamana
6. Calming	cittashamana
7. Thoroughly calming	cittavyupashamana
8. One-pointedness	cittaikotikarana
9. Equanimity, balancing	samadhana

Stages of meditative stabilization
Usually classified as four states of absorption (jhana/dhyana), each having two levels of access and achievement) and four formless attainments (samapatti). Taken together and preceded by one level to cover the training in steps leading to full shamatha, they are listed as nine levels of meditative stabilization, as follows.

	Stage or ground (skt. bhumi)	Name in Sanskrit
1	gross sensory experience	kama bhumi
2	first stabilization	prathama dhyana bhumi
3	second stabilization	dvitya dhyana bhumi
4	third stabilization	tritya dhyana bhumi
5	fourth stabilization	chaturtha dhyana bhumi
6	sphere of infinite space	akashanantya ayatana bhumi
7	sphere of infinite consciousness	vijnananantya ayatana bhumi
8	sphere of infinite nothingness	akincanya ayatana bhumi
9	sphere of neither cognition nor absence of cognition * summit of existence	naivasamjna naasamjna ayatana bhumi * bhavagra

While "dhyana" and "samapatti" have very strict, technical meanings, "samadhi" is a much more flexible term, covering many different states and stages in development of wisdom, compassion, and intensity, plus different perspectives in awakened awareness.

It seems useful to note here, that not all schools emphasize separate shamatha training: whether the emphasis on vipassana in some Theravada lineages (using khaṇikasamādhi), or the inseparability of samadhi and prajna in Ch'an/Zen, or the nonduality of relative and ultimate in Vajrayana, this approach has had mixed results for those practitioners who ignore the significance of the gradual approach in which stable concentration - whatever the definition: momentary, access, or fixed - is essential and requisite for effective practice.

Just for example, here's an explanation from a contemporary Ch'an master, explaining stages of combining calm and insight to guide his students in a method that traditionally does not conceive actual stages:

"...relaxing the body and the mind must come first, beginning with mindfulness of breath. Eventually, one’s awareness expands to the totality of the body. As one proceeds with this practice, the body may start to dissolve. The felt sense of the body will start to be so subtle that it will hardly be perceived. After that, even the body disappears, but the external environment is still present and one’s field of awareness expands to include the immediate surroundings of the meditator. Then, the external environment can also be dissolved. The mind’s awareness becomes expansive and is not focused on particulars in the external environment. Gradually, the mind becomes unified with the external environment. At this time, this unified self, taking in all things in the environment, is doing the sitting. But even this unification, this stage of oneness, must be let go of, put down. When this oneness—the identity of the external environment with oneself—is put down, the great self is also dropped away. When the self drops away, that is precisely the[...] stage of maha-shamatha-vipashyana, the inconceivable realm."

Or, in another context, even more concise:

"...real progress is always gradual and involves stages. First, learn how to concentrate the mind. Through concentrated mind, you can further unify the mind. Then you can dissolve and melt away your unified mind to attain no-mind, or enlightenment. So these three stages-concentrated mind, unified mind, and no-mind-come through gradual and focused practice."

As we see, shamatha may be presented as an early stage of vipashyana, without even separating the two. So, talking of progress through stages, even when the analytical mode is pursued from the very onset, some concentration will have to build up untill reaching a stage of unification and non-distraction, which then serves as basis for advanced insight practice.

More notes to follow.