Without our knowlege, our landlord gave someone a key to our home who let someone in. No notice or explanation was given. Do we have legal recourse?

What happened to you is, I am sure, very upsetting and gives you a feeling of not being safe in your home.  But your question needs more details to answer.  First, you need to read your lease.  Most leases have a provision in it for landlords to enterthe apartment, the type of notice needed (phone call?), etc.   In cases of emergency - like a pipe bursting - that notice may not always be possible and as long as he/she acts reasonably under the circumstances,  the landlord would be allowed to enter. Landlords have a right to protect their investment.  If the landlord could not be there to let in someone he/she could have an "agent" - someone who does something on their behalf - do it for him.  That being said, at the very least here you have the right to an explanation of why they were in the apartment and who was let in.  Look in your lease as I said and try and find the paragraph I mentioned.  Once you have all the information let your landlord know that he/she did/ did not follow the correct procedure for access to the apartment ("why" here)  and that in the future you expect that he/she will give you proper notice, etc.  You may want to tell the landlord verbally and follow it up with a formal letter.  If it doesn't stop then you may need to see an attorney to read the lease carefully to see if the actions amount to a breach or what other legal remedies you have in Indiana.