To find the value of \( M \) given by the expression \( M = 100^2 - 99^2 + 98^2 - 97^2 + \ldots + 2^2 - 1^2 \), we can use the difference of squares formula. The difference of squares formula states that:

\[
a^2 - b^2 = (a - b)(a + b)
\]

Applying this to each pair in the given expression:

\[
100^2 - 99^2 = (100 - 99)(100 + 99) = 1 \cdot 199 = 199
\]
\[
98^2 - 97^2 = (98 - 97)(98 + 97) = 1 \cdot 195 = 195
\]
\[
96^2 - 95^2 = (96 - 95)(96 + 95) = 1 \cdot 191 = 191
\]

Continuing this pattern, we see that each pair \( (a^2 - b^2) \) simplifies to \( (a - b)(a + b) \), which is always \( 1 \cdot (a + b) \). Therefore, each term in the sequence is simply the sum of the two numbers in the pair.

The sequence of sums is:

\[
199, 195, 191, \ldots, 3
\]

This is an arithmetic sequence where the first term \( a = 199 \) and the common difference \( d = -4 \).

To find the number of terms in this sequence, we use the formula for the \( n \)-th term of an arithmetic sequence:

\[
a_n = a + (n-1)d
\]

Setting \( a_n = 3 \):

\[
3 = 199 + (n-1)(-4)
\]
\[
3 = 199 - 4(n-1)
\]
\[
3 = 199 - 4n + 4
\]
\[
3 = 203 - 4n
\]
\[
4n = 200
\]
\[
n = 50
\]

So, there are 50 terms in the sequence. The sum of an arithmetic sequence is given by:

\[
S_n = \frac{n}{2} (a + l)
\]

where \( l \) is the last term. Here, \( n = 50 \), \( a = 199 \), and \( l = 3 \):

\[
S_{50} = \frac{50}{2} (199 + 3) = 25 \cdot 202 = 5050
\]

Therefore, the value of \( M \) is:

\[
M = 5050
\]