1. If the hash algorithm is properly designed and distributes the hashes uniformly over the output space, "finding a hash collision" by random guessing is exceedingly unlikely (it's more likely that a million people will correctly guess all the California Lottery numbers every day for a billion trillion years).
This astonishing fact is due to the astonishingly large number of possible hashes available: a 128-bit hash can have 3.4 x 10^38 possible values, which is:
340,282,366,920,938,463,463,374,607,431,768,211,456 possible hashes

2. atoms in the universe = 1078 to just under 1081 =
1 gig numbers / sec
1 gig = 10^9 = 2^30
128 bit will take 2^98 secs
= 2^73 years
= 10^20 years
100,000,000,000,000,000,000 years
(1 year = 2^25 secs)
atoms in the universe = to just under 1081 =
i.e to 2256

4. Merkle Damgard Compression
e.g. MD-5 uses 512 blocks of messages per round of compression, each broken into 4 stages (128 bits)

5. One MD5 operation.
MD5 consists of 64 of these operations, grouped in four rounds of 16 operations. (A,B etc = 32 bits)
F is a nonlinear function; one function is used in each round.
Mi denotes a 32-bit block of the message input, and Ki denotes a 32-bit constant, different for each operation.
<<<s denotes a left bit rotation by s places; s varies for each operation.
+ denotes addition modulo 232.

6. Hash collisions Thought to be impossible
Only one known so far for a “good” algorithm
MD5 hash collision

7. SHA-1: 160 bit hash
Start with 512 bit blocks of input, pad it if needed.
Expand to bit subkeys (Wt)
Initialize some hash blocks (A, B, …E)
Use input to generate Wt, Kt is a constant.
F is a changeable functions, constructed from shifts, and XORs.
Do 80 rounds. Then use more input.
Can be made to be fast.