According to Wikipedia:
Although the content is similar to the Discourses of Epictetus, it is not a summary of the Discourses but rather a compilation of practical precepts. Eschewing metaphysics, Arrian focused his attention on Epictetus's work applying philosophy in daily life.
So, chapter 1 says:
Some things are in our control and others not. Things in our control are opinion, pursuit, desire, aversion, and, in a word, whatever are our own actions. Things not in our control are body, property, reputation, command, and, in one word, whatever are not our own actions.
So I take pursuit, desire, and aversion to not just be things of the mind, but those same things manifested into action.
Work, therefore to be able to say to every harsh appearance, "You are but an appearance, and not absolutely the thing you appear to be."
Use this line to separate the internal from the external. We have control over the internal, don't confound the two.
Chapter 3:
With regard to whatever objects give you delight, are useful, or are deeply loved, remember to tell yourself of what general nature they are, beginning from the most insignificant things. If, for example, you are fond of a specific ceramic cup, remind yourself that it is only ceramic cups in general of which you are fond. Then, if it breaks, you will not be disturbed. If you kiss your child, or your wife, say that you only kiss things which are human, and thus you will not be disturbed if either of them dies.
Wow, this guy is harsh. But it reminds me of a passage used in How To See Yourself As You Really Are (page 34) by His Holiness the Dalai Lama. This particular passage comes from Nagarjuna's Sixty Stanzas of Reasoning:
How could great poisonous afflicitve emotions not arise In those whose minds are based on inherent existence? Even when an object is ordinary, their minds Are grasped by the snake of destructive emotions.
Chapter 4 proposes that every activity be done with a dual purpose. Go to the bath house to bath and to maintain a calm mind.
Wikipedia uses chapter 5 as a summary for the work. It demonstrates that things which bother us can also be broken down into the two categories of the first chapter. Then we see that men are disturbed "by the principles and notions which they form concerning things."
Chapter 10 concerns making the best of accidents: "ask yourself what abilities you have for making a proper use of it." "And thus abituated, the appearances of things will not hurry you along with them."
Chapter 11 concerns not mistaking you have a right to possessions.
Chapter 13:
If you want to improve, be content to be thought foolish and stupid with regard to external things. Don't wish to be thought to know anything; and even if you appear to be somebody important to others, distrust yourself. For, it is difficult to both keep your faculty of choice in a state conformable to nature, and at the same time acquire external things. But while you are careful about the one, you must of necessity neglect the other.
I rather enjoy Chapter 15. "Remember that you must behave in life as at a dinner party." Basically don't go charging for the food, but treat them as a pleasant addition. Treat all your desires the same.
Chapter 20 echoes that of chapter 5.
Chapter 22 on studying philosophy, but really anything:
For remember that, if you adhere to the same point, those very persons who at first ridiculed will afterwards admire you. But if you are conquered by them, you will incur a double ridicule.
Chapter 25 says "don't be jealous." It continues that wanting someone else's achievement is equivalent to working/striving as they do for it. In the past you decided not to go that route, do not wish for something without the consequences. I don't think the second part of this chapter should be read in terms of privilege, but in terms of wishing you magically had another's interests.
Chapter 26: Treat your misfortunes just as you treat others'.
Chapter 29: Don't over-commit. Think about what a course of action requires.
Chapter 30: Duties are universally measured by relations.
Chapter 32: Don't worry about prophesies, they just concern things which we can't control.
Chapter 33: How to act in public. I enjoyed reading this one:
If anyone tells you that such a person speaks ill of you, don't make excuses about what is said of you, but answer: " He does not know my other faults, else he would not have mentioned only these."
When you are going to confer with anyone, and particularly of those in a superior station, represent to yourself how Socrates or Zeno would behave in such a case, and you will not be at a loss to make a proper use of whatever may occur.
Chapter 34: Temptations of pleasure.
And even though it should appear to you a seasonable gratification, take heed that its enticing, and agreeable and attractive force may not subdue you; but set in opposition to this how much better it is to be conscious of having gained so great a victory.
Chapter 35: Never shun being seen doing the right thing.
Chapter 40: Discouraging the objectification of women, though I don't want to read too much of my own time into Epictetus's writing.
Women from fourteen years old are flattered with the title of "mistresses" by the men. Therefore, perceiving that they are regarded only as qualified to give the men pleasure, they begin to adorn themselves, and in that to place ill their hopes. We should, therefore, fix our attention on making them sensible that they are valued for the appearance of decent, modest and discreet behavior.
Chapter 42: On dealing with people who are wrong.
Therefore, if he judges from a wrong appearance, he is the person hurt, since he too is the person deceived. For if anyone should suppose a true proposition to be false, the proposition is not hurt, but he who is deceived about it.
Chapter 45: Think before you judge.
For, unless you perfectly understand the principle from which anyone acts, how should you know if he acts ill? Thus you will not run the hazard of assenting to any appearances but such as you fully comprehend.
Chapter 46: Don't call yourself a philosopher, produce as a philosopher.
And, if anyone tells you that you know nothing, and you are not nettled at it, then you may be sure that you have begun your business. For sheep don't throw up the grass to show the shepherds how much they have eaten; but, inwardly digesting their food, they outwardly produce wool and milk. Thus, therefore, do you likewise not show theorems to the unlearned, but the actions produced by them after they have been digested.
Chapter 47: "don't grasp statues, but, when you are violently thirsty, take a little cold water in your mouth, and spurt it out and tell nobody."
Chapter 50: "And if any instance of pain or pleasure, or glory or disgrace, is set before you, remember that now is the combat, now the Olympiad comes on, nor can it be put off."
Finally, my favorite poem from chapter 52:
"I follow cheerfully; and, did I not, Wicked and wretched, I must follow still Whoever yields properly to Fate, is deemed Wise among men, and knows the laws of heaven." Euripides, Frag. 965