Below are the basic lines of the hand:

The information and pics on lines provide by: Mystic India

The line of Life :

The line of life, is the line which, rising under the Mount of Jupiter, goes down the hand and embraces the mount of Venus. On it is marked time, also illness and death, and events foreshadowed by the other important lines are verified. If the Line of Life is semicircular, thin and deep, without irregularities, breaks, or crosses of any kind, it is an auspicious sign and promises long life, good health, and vitality. A thick, shallow and straight line of life is not auspicious.

The line of Head:

The line of Head relates principally to the mentality of the subject - to the intellectual strength or weakness, to the temperament in its relation to talent, and to the direction and quality of the talent itself. It is indicative of the mental level or the intelligence of a person. Whether a person would have money or not is also divined from a study of this line. If one goes a little deeper into things one finds that intelligence or a person's mental level has something to do with whether he would have money or not. If a person loses the capacity to act intelligently, he is sure to lose whatever money he has and, conversely, using one's wits fully can lead to affluence.
This line generally originates from a point between the Aggressive Mars and the Mount of Jupiter and terminates at the Defensive Mars, but in most palms it is seen beginning from the Mount of Jupiter or the Aggressive Mars of the Line of Life and terminates at the Mount of Mercury or the Mount of Luna. The point of origin and the point of termination of the line enter into its effect on the life of the individual.

The Line of Heart :

The line of heart is naturally an important line in the study of the hand. It is believed to be line of emotions. Love or the attraction of the sexes from natural causes plays one of the most prominent parts in the drama of life, and as in the nature so in the hand. The Heart Line is the horizontal line above the Headline. It begins beneath either the index finger or middle finger and extends across to the edge of the palm on the side of the little finger.

The Fate Line:

The Line of fate, also known as line of destiny, or the Saturnian's, is the center upright line on the palm of the hand. In consideration of this line the type of hand plays an important part; for instance the line of fate, even in the most successful hand is less marked on the elementary, the square, and the Spatulate, than on the philosophic, the conic, or the psychic. Consequently if one sees, as one often will, an apparently very strong line of fate on a conic hand, one must remember that it ha snot half the importance of a similar line on a square types as far as worldly success is concerned.

The Line of Health:

This line rises at the base of Mount of Mercury, and as it grows down the hand and into the line of life, so does it foreshadow the growth of the illness or germ of disease which at the time of its coming in contact with the line of life will reach its climax. It should lie straight down the hand - the straighter the better. Although it is an excellent sign to be without this line. Such absence denotes an extremely robust, healthy constitution. Its presence on hand in any form indicates some delicate point to be guarded against.

The Marriage/Sex line:

If the line is straight, it is generally indicative of a good marital relationship or an enduring love affair. If this line inclines towards the Heart Line it indicates an interruption with marital relations or ill health of the spouse. If this line inclines towards the little finger, the spouse is likely to have a long life. This line may not be single one, but there might be two or even three such lines.

But it does not mean that a person would have as many marriages or love affairs. It would suffice here to point out that sexual or marital relations or love affairs are not to be inferred from this line alone. One must study the line of Mars, the line of Saturn; the Line of the Sun, the Mount of Venus and the Mount of Jupiter before answering any questions about marriage or its breakup.

Children lines:

Circular shape of the Line of Life .The number of islands at the base of the thumb the branches at the end of the Heart Line. Parallel lines near the base of the thumb.

Line of Mars:

Some palmists believe that it is a line of influence of the Mount of Venus. It is a parallel line within the Line of Life. If it is very near the line of life or if it is very deep it indicates the extent to which a person is subject to fits of anger. If it is away from the Line of Life the person is likely to be of an equable temper. It also indicates the state of marital relations. It originates from the Aggressive Mars, runs parallel to the Line of Life towards the Mount of Venus and terminates at the wrist or the Mount of Venus.

Also there are many side lines but those up are the most asked.