Though one will find tremendous variation in the way that Pilates exercises are presented today, there is a traditional order to the Pilates mat exercises, as developed by Joseph Pilates. Below are samples of the first 10 exercises of a classical Pilates mat workout. At the end of this first 10 exercises, which is meant to be an introduction to the classic order, you will find a list of the rest of the exercises in a traditional level 1 program.

courtesy of Peak PilatesThough the exercises in the traditional set are all level 1 exercises, you will see that the program below is a challenging workout, especially for the abdominals. Most classes will precede this program with some
warm-up fundamentals. I have also added
modification reminders for each of the exercises to assist those who are beginning to develop their
core strength or have physical challenges.

courtesy of Peak PilatesThe hundred builds core strength, stamina and coordination. To do this exercise you must fully engage the abdominal muscles as you practice a dynamic breathing pattern.
Modifications for the hundred include working with the legs higher,
table-top legs, and leaving the head down.

(c)2007, Marguerite OgleRoll Up is a great challenge for the abdominal muscles, and a wonderful articulation for the spine. It has been said that one well executed Roll Up is equal to six regular sit ups, and is much better than crunches for creating a flat stomach.
Supported roll back and
chest lift are good training exercises for Roll Up.

(c)2007, Marguerite OgleOne Leg Circle challenges core stability, as one must keep the entire trunk -- including the hips -- still as one leg circles independently.
Modify one leg circle by having the non-working leg bent with the foot flat on the floor. The knee of the working leg can also be slightly bent.

by Peter Kramer, courtesy of Kolesar StudiosThe first of the rolling exercises, rolling like a ball stimulates the spine, deeply works the abdominals, and tunes us into the inner flow of movement and breath in the body.
Modifications for rolling like a ball include holding the thighs behind the knees and opening the legs further out from the body. Do not do rolling exercises if you have back or neck problems.
Read:
Tips for Rolling Exercises.

courtesy of Peak PilatesSingle leg stretch is often cited as an exercise that helps target the lower abs. Of course it works the entire core, requiring strength and stamina as one maintains an upper body curve and keeps teh torso stable while switching the leg and arm positions.
Modify single leg stretch by leaving your head down or working with your legs higher.

(c)2007, Marguerite OgleGoing for even more abdominal strength and endurance, we follow single leg stretch with Double Leg Stretch. Double Leg Stretch is a graphic way to experience working from the center of the body as the arms and legs reach away and return together.
Develop this exercise by working the arms and legs with the head down at first.

courtesy of Kolesar StudiosSingle straight leg stretch keeps you working the core and adds a stretch for the hamstrings. As with many of the previous exercises, the legs are moving without affecting the stability of the torso.
Modifications for this exercise include leaving the head down, grasping the leg below the knee, bending the knees slightly, and increasing or decreasing the distance between the legs.

by Peter Kramer, courtesy of Kolesar StudiosDid somebody say core strength? If you are following along in sequence, you have done 4 intense ab exercises in
forward flexion in a row, and 6 since we started. But don't stop now, just keep your form. Attention to form will protect your back. Double leg lower/lift will challenge your abs and tempt your lower back off the mat. Don't let it.
Modify by keeping your head down and/or by keeping the legs high.

(c)2007, Marguerite OgleWorking an upper body rotation against a stable pelvis is an excellent workout for the abs, but the rotation requires extra work from the obliques. Working the obliques supports posture and the ability to flex and rotate the torso. It's also a waist whittler.
A modification for Criss Cross is to have both legs in table top position and only work the upper body.

Courtesy of Peak PilatesSpine Stretch is a Pilates mat exercise that feels really good. Though it is still a flexion exercise done with the abs lifted, the emphasis has changed to stretching the spine. Spine stretch can also be a stretch for the hamstrings as well as a moment to center oneself before moving on to more challenging exercises.
Spine stretch rarely needs much modification, but those with tight hamstrings may want to sit on a small lift or have the knees slightly bent. Spine stretch can also be done with the arms lower, finger tips along the floor.
While there is some disagreement among Pilates camps as to what the exact order should be, basically the rest of the traditional Pilates mat sequence is as follows:
Free instructions for most Pilates mat exercises can be found in the
Pilates Exercises folder here at pilates.about.com.