The only reason a fuse blows is because it got overloaded(too much amps). Most lawn/garden tractors use separate soleniod for the starter and you said it blows a fuse as soon as you turn on the key. At that point the starter wouldn't(or shouldn't) have any current to it at all. A stuck on soleniod would keep the starter engaged till you unhooked one of the battery cables. Find what that fuse protects in electrical system and start looking for bare wires, maybe a wire has rubbed through where it's laying against metal or a mouse?

What's the Sears 917.xxxxxx number?

Obviously you have a short "somewhere" and we need to isolate it.
For troubleshooting purposes, I recommend making up a 12V test light (from an old fuse?) that you can insert in the fuse holder.
IF the tractor has an ammeter, try bypassing it. I'm aware of one (Craftsman) instance where the ammeter got moisture in it and would short to ground when the needle moved.

I have a voltmeter that I bought today. Will that work instead of the test light. If so, how do I use it? I don't know how to by pass the ammeter. Got suggestions.

Sears number is 917271024

You could unplug several connections at once, re-hook them 1 at a time until the fuse blows. Headlights are high on the list of shorting as well.

can I just crank the engine over and mow the lawn and worry about the fuse another time, or will it burn something out?

Your tractor has 2 Operator Presence Relays (OPR)
They are Bosch relays, which look like this.
{{gwi:328174}}

Pins will be numbered 30, 85, 86, 87 & 87A.
IF either isn't "activating", it will blow the fuse.
Temporarily, unplug both of them.
OPR1 contains the kill circuit for the engine. However, the fuel shutoff solenoid will also kill the engine. Just not as fast.
OPR 2 is for the stator brake. Without it, the engine will not stop as fast.

Examine the plugs closely. A burned contact may prevent proper operation, resulting in a short.

You can get these relays at an auto parts store for much cheaper than a "tractor store".

NEITHER are needed to operate. They are for safety reasons!!
Those would be the likely suspects.

The only other places that would possibly short (other than a melted wire) would be seat, clutch and attachment clutch switched. They would pretty much have to be "broken".

I hope it works - If I don't post you'll know I ran into problems with the safety stuff!

I disconnected the DC ampters wires - there were two - now the fuse does not blow, but the mower does not start. Reconnected them and the fuse blows. "very interesting"

I just checked the + wire going up from the fuse to where the 2 leads go into the dc amperes meter. There was nothing registering. It appears that from the B side of the fuse holder (which is hot from the battery)there is a little over 12 volts (like 12.47) The A side of the holder leads up to the amperes meter which is marked +. On the other side of the amperes meter there is another wire (both are red) which leads back to the main string of wires and appears to go to the ignition switch.

I kept the machine off - replaced the fuse with new fuse - and then pulled the + wire from the amperes meter and put the red probe into one or the circles of the clamp and used a screw on side of machine for ground. NOTHING THERE - I am assuming I tested the meter correctly. I just left the other wire that goes to the ignition switch alone.

I am wondering why there is no juice up there

I checked the other side that is NOT marked +. It was hot. Thought despite the + on the wire that it was not +. I reversed the wires. I turned it on and it blew the fuse, back to the store for a case of fuses. Out of ideas. why is there a surge or whatever to the fuse? Seems like I would have to have it serging before it got to fuse - why does it only blow when an attempt is made to turn it on.

"I disconnected the DC ampters wires - there were two - now the fuse does not blow, but the mower does not start. Reconnected them and the fuse blows. "very interesting"

Not really. It's basically the same thing as disconnecting the battery cable.

IF you unplug THE OPR's, you REMOVE some of the likely places the wiring is SHORTING and help ISOLATE the PROBLEM!
Is that too expensive for you?

IF you have a soldering iron, make up a 12V test lamp with the tabs from a "dead" fuse and use that in place of the fuse.
Then you can eliminate shorts by unplugging various wires and seeing when the light goes out.
Or invest in a fuse company!

To see IF the ammeter is the problem, unplug it and jumper the 2 wires together. IF it still blows a fuse, it wasn't the problem.

Got it started. Turned out to be a lose connection or dirty pins - something like that, as when I cleaned it - It worked.

Thanks for the advice. I wouldn't have known what to do without it.

Lose connection or dirty connections on what? What did you clean???

I have replaced the starter,solinoid,baterry &key switch and it keeps blowing my 20 amp fuse

if you know elect troubleshooting, isolate the condition/circuit that is causing the fuse blowout; then search for the improper ground fault.
If above is greek, take tractor to a qualified shop for service/repair.