Think numbers... er, letters... and numbers...
1. 3 3 5 4 4 3 5 5

Each number represents the number of letters in the number in that order. That is: one = 3, two = 3, three = 5, etc.

Skipping through the week, do the same thing with this series:
2. 6 9 6 6 7 8

Each number represents the number of letters in a day of the week, skipping days. So Monday, Wednesday, Friday, Sunday, Tuesday, Thursday.

We simply travel forward through time, but numbers...
3. 1 2 13 0 3 03 1

The number of days in each month, but only the second digit is given for January, first digit for February, March is backward, and then the series repeats, beginning with April.

The same can be said for letters...
4. A F AM P M UJ U

Same logic as in probelm 3, but using the first 1 or 2 letters in the name of each month.

If you've solved all of those, this should be easy:
5. 7 5 3 4 9 8

Number of letters in each month, but skipping a month each time. So January = 7, March = 5, May = 3, and so on.

This is where I live, and yes, it often appears to be mixed up. But there is a logic to it:
6. n t d s a e . f a e i a u i e .

Skipping a letter each time, the series spells out most of "United States of America". After the last a in America, the series begins again with u in United. The twist is when skipping, if the next place skipped to is a space, a . is substituted instead.

A patriotic series:
7. w a j m m a j

The first letters of the last names of each of the first 7 US presidents.

What number is missing from this series?
8. 2 3 5 7 13 17 11

The series is of the first prime numbers, and 11 was left out.

If you saw what I was up to in the last problem, it should help you now:
9. 15 11 9 5 3 1 0

The series is of the prime numbers in reverse order, beginning with 17, but 2 was subtracted from each number.

It's elementary, my dear puzzler
10. h l b n f n a p c

The first letters of the odd numbered elements on the Periodic Table, from 1 to 17.

Series puzzles can come in different shapes and sizes:

11. 5 8 7 13 2 6
2 15 3 20 4 10

For each number square, take the difference between the top 2 numbers, and divide it by the number in the bottom left corner. Multiply the resulting number by 10, and write it in the bottom right corner.

The numbers that represent a letter of the alphabet form that number. The last letter is made up 20's, forming the letter T.

13. 60 90 90 120 120
120 120
60 60 90 90 120 120

The angles in the first figure, a triangle, total 180 degrees. 180 divided by the 3 angles = 3 60's. The square or rectangle is formed from angles totaling 360 degrees. And the final shape, a hexagon, is made up of 720 degrees. The formula for finding the number of degrees in a shape is (X - 2) 180, where X is the number of sides/angles in the shape. You could have replaced the ?'s in the last shape with basically any numbers you wanted, as long as they total 720.

Find the sum of the numbers in each shape, and then multiply them by the number of sides/angles in that shape. The resulting number is written where each of the points would be on the next shape, which is then used to calculate the number for the next shape, etc.