Part 1
Core muscles that work well in movement are the prerequisite for
optimal power transmission, so having a strong core is essential to
going faster on the bike.
You can make your legs as strong as you like, but if you don't have
stability in your torso to apply force to the pedals, are you really
going as fast as you can?
No.
A strong and stable core can help you be more efficient, will allow
you to transfer more power through the legs, reduce the instance of
injury, improve your posture, as well as fight fatigue on long days.
Plus, adding in some weight bearing and loading exercises is good for
bone health.
As a general rule most riders disregard spending time training in this
area: we'd rather devote more time to hours in the saddle.
However, one or two sessions a week can go a long way in boosting
power and keeping us on the bike.
Bottom line?
Seems like a good idea to start incorporating some core work,
especially as we now have some off the bike time.

There are a lot of core training plans out there, but here are some basics:

Core work should ideally be done 1-3 times per week, and gradually
reduced to 1 time a week by the build phase for maintenance sake. Some
athletes need more core work though, so always do what works best for
you. It also helps to do these in front of a mirror the first few
times so you can spot any breakdown in form/weakness. Always try to
maintain good form throughout the exercises and if you do notice a
breakdown, stop.

1. Plank

The plank is one of the best exercises for the core. It’s something
you can build up to, and will definitely help you generate additional
power and stability while on the bike.
Start in a push-up position.
Put both your elbows on the floor with your forearms parallel.
As you keep your body flat, you should engage your core. Don’t arch your back.
If this is your first time doing a plank, start with 30-60 seconds,
then gradually build up to a minute or two, and repeat.

2. Burpees

You might remember these from gym glass, but they are a great little
workout for a cyclist, especially in the off-season.
Stand with your feet shoulder-width apart.
Next, squat down and place your hands on the floor in front of you,
and be in a push-up position.
Jump your feet in towards your hands.
Jump into the air and straighten your arms all the way overhead.
Do a series of those and you’ll feel it.

3. Lateral walking push-ups

This takes your regular push-up and increases the difficulty.
Start with a push-up then take a lateral step to the side while in
plank position.
You can mix it up by moving in one direction repeatedly, or move back
and forth between each one.

4. Russian twists

Although this sounds like the name of a great cocktail, it certainly is not.
Begin by sitting on the floor with your knees bent.
Gradually lean back and you will begin to engage.
Next, twist your torso to one side and return to the centre, then
repeat on the other side.
Try to do 10-15 reps for each set.

5. Hollow Holds

Hollow holds are a great exercise as they not only activate the abs
and hip flexors but your quadriceps too.
Begin on your back, with your feet together and arms overhead.
Activate your core by simply pushing your lower back down into the ground.
Raise your arms and legs off the floor. Now, try and hold this
position for several seconds.