Stretching and Core Exercises:

Stretching:

Benefits from stretching are much debated, but I have to believe it helps to optimise muscular contraction and promote recovery. My logic is simple: Myosin fibres in muscle need to be optimally alined to produce the most powerful contraction. So both over stretching and the muscle fibres being too tight is bad.

• When stretching take care to stretch muscles in "antagonistic pairs" where possible. I.e. the quadriceps, then the hamstring.
• Tensing the muscle and then stretching I find also help the muscle loosen up, relax and accept the stretch.
• Never "bounce" keep the stretch smooth.
• It shouldn't be painful, just so you can feel pressure, but not a tearing heat.
• A stretch should be held for not longer than 25 seconds. 

Core Exercises:

Core exercises are important not just to cycling, but life in general. The dreaded sore back is usually caused by insufficient core strength. Keep things simple, do not over do any one exercise. It's very easy to over do sit ups for example and then be unable to train them for several days.

• As with stretching I like to do my abs and then my back (Sit ups followed by Lumbar extensions). I usually do 30 reps three times.
• After you have built up to the 90 reps per session,  repeating the session twice a week is enough to maintain the gains in tone and strength you have achieved.
• Lats are important to too: these can be done by holding a heavy weight in one hand, standing straight and leaning slightly over to the side of the weight, then returning to standing straight. I do 20 repetitions three times.

Here is a very complete article on core exercises: https://www.bicycling.com/training-nutrition/training-fitness/core