To determine who serves first, you flip a coin or (more likely) spin a racket. Whoever wins the toss gets to decide one of four things: that she wants to serve first, that she wants to receive first, which side of the court she wants to start on (in which case, the opponent chooses who serves first), or that she wants to leave the choices up to her opponent.
This discussion is very timely for me because not only is it helping me stabilize my game, my daughter is now six and showing interest in “Playing tennis.” When she was four and five that meant catching and sweeping the ball along the floor with a racket back and forth with me, and now it means gripping the child’ racket her aunt brought her with both hands and hitting FH on the soft coach’s ball I toss or hit softly to her. She is a natural leftie, and I showed her a LH grip with two hands, but often she uses the RH backhand grip instead, and I just let her go with it. What is amazing to me is how good her balance is and how well she steps in and rotates through the stroke, pulling the racket through. She is already an accomplished dancer and seems to understand how her body moves, and that clearly helps, but her synthesis of gripping, which she was taught, swinging, which she imitates, and rotating with balance is just natural.
I focus on the student ability to improve skills in the court by having constant repetitions of drills. I also make the lesson more attractive for the students by playing with them and make them experience real game practice.  I structure my lessons with short warm up continued by certain amount of drills and finally different games applied to different situations of the game. 
So, a lot of people are very competitive in everything they try. They want to have the best business if they get into it, they want to be the best at their job when they get it, etc. If you are that sort of person and you look for excellence in your game but do not want to commit professionally to this then it is going to take an upwards of 5-10 years to play at some decent level like club level or USTA sponsored tournaments.
Most people aspire to get to this level without wanting to go full time on tennis. And it seems to be pretty achievable. You can expect a 1-year learning phase and slowly rise to a pretty good intermediate player by your 5th year. That being said, you must be willing to work hard and accept some criticism from peers. You must develop your technique either from paid coaching or from Youtube Lessons and practice them on the court.
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Another alternative set format are so called "short sets" where the first to four games to win by two games. In this format a tie-break is played at four games all. The ITF experimented with this format in low level Davis Cup matches, but the experiment was not continued. Nevertheless, this alternative remains as an acceptable alternative in the ITF rules of Tennis.[32]
Sportswriter John Wertheim of Sports Illustrated stated in an article in July 2010 that Serena Williams is the greatest female tennis player ever with the argument that "Head-to-head, on a neutral surface (i.e. hard courts), everyone at their best, I can't help feeling that she crushes the other legends.".[120] In a reaction to this article Yahoo sports blog Busted Racket published a list of the top-10 women's tennis players of all time placing Martina Navratilova in first spot.[121] This top-10 list was similar to the one published in June 2008 by the Bleacher Report who also ranked Martina Navratilova as the top female player of all time.[122]
I accept your thesis — kids & adults learn tennis differently. But there’s a corrolary: As someone who began tennis 10 yerars ago as a retirement activity, I’m confronted by others in my over-70 age group who — I swear — began hitting tennis balls before they could walk. There’s no way I can catch up with them. Should I give up, & just play with others “at my level”? [This is a serious question.] Or should I attempt one-person drills with the aim of improving?
Again, begin with the grip. Whether you choose to use a one handed backhand or a two handed backhand, it’s important to grip the racket closer to the top bevel with your dominant hand. For a two handed backhand, the non-dominant hand should grip the racket underneath the handle, and keeping your palm rested firmly on the racket handle. Fingers should be free of tension, and not too close together. The grip for the two hander should have your other hand adjacent to the first. It’s necessary to practice both the forehand and backhand tennis strokes as you learn to play tennis.
During the 19th century the Royal Tennis Court played a variety of different roles. It served as a theatre storeroom, a workshop and storage space, and a studio for the painters Antoine-Jean Gros and then Horace Vernet. It was listed as a national monument in 1848, then became a games room again under the Second Empire. Approaching the centenary of the oath, under the Third Republic, architect Edmond Guillaume was invited to restore it and convert it into a museum of the French Revolution. The architect used original engravings to reconstitute the spirit of the room, which had been modified and had deteriorated over the course of the century. The museum housed the statue of Bailly, busts of the most important signatories of the oath, and a monumental canvas by Luc-Olivier Merson, based on Jacques-Louis David's preparatory drawing. The museum was inaugurated on 20 June 1883 in the presence of Jules Ferry.
We’ve now covered scoring, the first step to learn as a tennis beginner — let’s move on to understanding the court. A tennis court is 78 feet long by 27 feet wide, and divided in half length-wise by the net. At each end of the court, there are white baselines — here, the serves are taken. These are also the out-of-bounds lines — a ball must not bounce beyond them or it’s out and the player who hit the ball loses a point.
The decision to install a top-of-the-line concrete court is just the beginning, however. You also need to evaluate your site, determine the type of playing surface you want, choose a surfacing system, and even pick out a color scheme. The next step is to find a qualified, experienced contractor who can install the court you want at a fair price. Here are some of the basics you need to know before getting in the game.
Between 1859 and 1865 Harry Gem, a solicitor and his friend Augurio Perera developed a game that combined elements of racquets and the Basque ball game pelota, which they played on Perera's croquet lawn in Birmingham, England, United Kingdom.[10][11] In 1872, along with two local doctors, they founded the world's first tennis club on Avenue Road, Leamington Spa.[12] This is where "lawn tennis" is used as a name of activity by a club for the first time. After Leamington, the second club to take up the game of lawn tennis appears to have been the Edgbaston Archery and Croquet Society, also in Birmingham.
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