Modes are tone groups, also called scales. One way to understand modes is to use a scale that we know, such as the C Major scale. Then, play the scale using the different tones in the scale as ‘starting points’. The Major scale has 7 tones, & all of them can be a ‘beginning point’ for a scale. All 7 are ‘starting points’. Yet, ‘starting points’ are just a concept. We don’t have to ‘start’ on a particular tone to produce the modal flavors [because the underlying harmony determines how melodic tones are perceived, unless there isn't harmony present].
Modes are scales with special names. Scales with particular flavors. The 7 modes derived from the Major scale system are named after early Greek tribes [the Ionians, the Lydians, etc.]. Modes have become almost mythic in their status. There is no proof that the Dorians used only the Dorian mode, or that the Phrygians only used the Phrygian, etc. Modes have an interesting history which you can read about on WikiPedia.
The basic rule for scales is that the number of tones in the scale is the minimum number of names that it can have. Every tone in the scale can be a root [or 1] for a scale. Since the Major Scale has 7 tones, there are 7 scales within the tone group. Again, every tone in the scale can be a ‘starting point’ [root]. When we play ‘tone to tone’ [e.g. D to D] in a particular key, we are playing in a new mode. Some dictionaries & musicians don’t use the word root for scales, yet we think it makes sense to do so. Semantics shouldn’t get in the way of using modes.
There are 21 basic modes [derived from the Major, Harmonic minor, and Melodic minor scale systems]. Here, we will be deriving only the Major scale's modes.

I - C Ionian [C Major] = c d e f g a b c
ii - D Dorian = d e f g a b c d
iii – E Phrygian = e f g a b c d e
IV – F Lydian = f g a b c d e f
V - G Mixolydian = g a b c d e f g
vi - A Aeolian [A Natural minor] = a b c d e f g a
viio – B Locrian = b c d e f g a b
In the beginning, we match up the modes with the corresponding harmony. This means when the Dm [the ii chord in C] is sounding, we are thinking & playing Dorian [the 2nd mode in C]. Yet, we don’t have to think D Dorian because if you are playing the Dm chord & soloing in C Major, D Dorian happens automatically.
Modes are melodic/tonal flavors. Ultimately, the harmony [if present] that we play melodic tones against determines how those tones are interpreted. Yet, we can think in any way that is suitable to us. We can think D Dorian even if the Dm chord isn’t sounding. These are called ‘subs’ [this is more advanced].
Again, the basic rule for scales is that the number of tones in the scale is the minimum number of names that it can have. Every tone in the scale can be a root [or 1] for a scale.
Since the Major Scale has 7 tones, there are 7 scales. Again, every tone in the scale can be a ‘starting point’. When we play ‘tone to tone’ [e.g. F to F], we are playing in a new mode.
We can also divide an octave with any tones within the octave span. Therefore, we can create your own modes. If modes we create aren't previously named modes, then we typically call them synthetic modes [scales we synthesized].
Ragas are melodic modes used in India.
The Major modes are Ionian, Lydian, & Mixolydian. The minor modes are Dorian, Phrygian, Aeolian. Locrian is a ‘diminished’ mode.
Note: Our research indicates that the Mixolydian mode was originally called the Lesbian mode until these modes became church modes. No explanation needed there. [If you know a different version of this, please share].
As explored in the Derivative/Parallel lesson, we can compare what is normal [what is derived - Derivative - from the Major scale system] to create names for the tones not in the key [the Parallel tones or non-diatonic tones]. Here we'll take a look at the formulas for the modes in a Major key, & the Major modes compared to the Major Pentatonic & then the minor modes compared to the minor Pentatonic.

Since the Major Pentatonic is 'missing' a 4 & a 7 tone. We can 'fill in' types of 4's & 7's to get the Major type modes that are in a Major scale system. Ionian, Lydian, and Mixolydian can be created by adding the appropriate type of 4 and 7 to the Major Pentatonic.

Since the minor Pentatonic is 'missing' a 2 & a 6 tone. We can 'fill in' types of 2's & 6's to get the minor type modes that are in a Major scale system. Dorian, Phrygian, and Aeolian can be created by adding the appropriate type of 2 and 6 to the minor Pentatonic.

Sometimes this is easier to track than trying to remember the modes in the order they appear in a Major key. This method is paralleling rather than deriving.