"If any one of you is without sin, let him be the first to throw a stone at her." (John 8:7)

Here is the situation surrounding this statement by Jesus:
The teachers of the law and the Pharisees brought in a woman caught in adultery. They made her stand before the group and said to Jesus, "Teacher, this woman was caught in the act of adultery. In the Law Moses commanded us to stone such women. Now, what do you say?" They were using this question as a trap, in order to have a basis for accusing him. But Jesus bent down and started to write on the ground with his finger. When they kept on questioning him, he straightened up and said to them, "Let any one of you who is without sin be the first to throw a stone at her." (John 8:3-7)

Is Jesus contradicting Moses?

The institutional temple teachers are testing Jesus' interpretation and application of instructions given by Moses at least 1,000 years earlier. This was a time when Moses led a people who were formerly enslaved through the desert after the Exodus. 

Tough rules helped keep the peace and keep people civil. There were rules that were necessary to keep those people calm. There were also rules (such as circumcision) that helped keep the Exodus people from becoming diseased or otherwise unsafe.

Yes, they were traveling through an inhospitable desert full of dangers and enemies. There weren't many ways to punish people who went overboard and harmed others. Tough penalties had to be instituted that suited the situation. They didn't have jails to keep people away from the others. So stoning was one of the few punishments scary enough to deter people from harming others.

Was Jesus contradicting this teaching?

According to Exodus and Deuteronomy, Moses gave instructions that helped the Israelites survive. Those instructions established the rule of law that allowed them to act in a civil manner. 

Traveling through the desert without the rule of law and facing threats all around them could tear the fabric of almost any group of people. So Moses presented rules according to the time and circumstance, to help provide the rule of law.

The ultimate intent of Moses in keeping the Israelites safe was to please the Supreme Being. While stoning is considered unacceptable in any civilized society, and certainly not pleasing to God, the practice may have been instituted originally to manage an untenable situation where the rule of law was necessary to keep people safe.

The primary purpose of the rule of law for the Israelites in the desert was to please God:
The Israelites did just what the LORD commanded Moses and Aaron. (Exodus 12:28)
This purpose was no different than Jesus' purpose with respect to his instructions. Consider this statement by Jesus:
"I am not here on my own, but He who sent me is true. You do not know Him, but I know Him because I am from Him and He sent me." (John 7:28-29)
This is clear that Jesus’ teachings were not coming from himself. “He sent me” makes the relationship very clear. The Supreme Being sent Jesus, and Jesus was representing the Supreme Being. Jesus’ teachings were coming from the Supreme Being. God was the source of Jesus’ teachings, and Jesus was His messenger.

Why are some of Jesus' instructions different than Moses'?

Some of God's instructions change due to time and circumstances.

In Jesus' time, the rule of law was much more established than in Moses' time. In the society of Jesus' time, there was a strong government that tried criminals and governed by a rule of law. During Moses' time, the Israelites were organizing themselves from living and traveling in the desert. They had previously been slaves in Egypt.

Basic rules grounded in fairness yet applicable to the survivalist situation were applicable. These rules were to prevent them from becoming wild animals that hurt each other and have sex with each other's husbands and wives. 

In that circumstance, God led Moses to establish rules and enforcement to create order. During Jesus' time, the Roman government combined with the Jewish system provided the rule of law that provided the enforcement. While stonings were still conducted - when decided upon by a council - Jesus recognized this government and rule of law. Consider Jesus' statement:
"Give to Caesar what is Caesar's, and to God what is God's." (Matt. 22:21)
So the time and circumstances had drastically changed, and the culture and society Jesus taught to had different needs than the culture Moses instructed. A government was already in place and enforcement was provided.

We can also relate the difference between Jesus' time and today's culture. For example, beatings, crucifixions, and stonings were common in Jesus' time for punishing criminals. In today’s society, we wouldn’t hear of such ghastly practices.

In the same way that society has changed since Jesus’ day, society had changed from Moses’ day to Jesus’ day. From Moses' to Jesus' times, the culture had also become more secular. Today, even more so.

The Supreme Being will adjust His specific instructions to the time and circumstance. The rules He establishes are not His key objectives. God is not setting up rules just to set up rules. He sets up rules and gives instructions through His loving servants to establish an environment that will encourage us to decide to return to Him.

Why does God want us back?

Because He loves us. He knows that we will only be happy when we are back with Him, sharing the relationship of love that we originally shared before we ate the forbidden fruit of envy. As symbolized in Genesis, once we ate the forbidden fruit of envy and wanted to enjoy as God enjoys, the Supreme Being sent us away to the physical world:
The LORD God made garments of skin for Adam and his wife and clothed them. (Genesis 3:21)
What are garments of skin? Are we talking animal skins? No, this is human skin. We are talking about the physical body - covered with skin. Because Adam disobeyed God and ate the fruit of self-centeredness, God banished him from the Garden of Eden - the spiritual world - and we took on temporary physical bodies (garments of skin).
So the LORD God banished him from the Garden of Eden to work the ground from which he [his physical body] had been taken. (Genesis 3:23)
Why were we banished? We were banished because we became envious of the Supreme Being. We wanted to enjoy like the Supreme Being. Consider this statement, made by God about Adam after he ate the fruit:
"The man has now become like one of Us, knowing good and evil. He must not be allowed to reach out his hand and take also from the tree of life and eat, and live forever." (Genesis 3:22)
What is "like one of Us," and what does "knowing good and evil" mean? Why would we want to become like God?

God created three types of individuals. One type is His direct expansions. These companions are imbued with all His power and authority ("Us"). The second is partial expansions - which have individuality yet are inseparable from Him as His constant companions. The third type is His separated expansions - each of us. We are also His companions but in the mood of loving servants.

Do we have the choice not to love God?

Yes. Without choice, love does not exist. This freedom of choice is symbolized by the trees of the Garden of Eden. There were different trees, but the tree of knowledge represented our choice to love God or love ourselves. The fruit that Adam and Eve ate symbolized their choice not to love God. Adam and Eve represent each of us.

'Knowing good and evil' means we wanted more. As clarified here, the correct translation of "good and evil" - טוב (towb) and רע (ra`) - is pleasure and pain - specifically self-centered pleasure and pain.

In other words, each of us fell from the spiritual realm because we were seeking to enjoy separately from the Supreme Being. The expression of this desire is self-centered pleasure, and the consequence of self-centered pleasure is pain.

Can we have one without the other?

The Supreme Being created the physical world - a world with duality - of pleasure and pain. This allows this world to teach us about the consequences of our choices. Yes, we are free to make whatever choices we want. But every choice and every action has a consequence. And every action has a reaction. This is one of the laws of nature intended to teach us.

We must remember that Adam was given the choice of whether to eat the symbolic fruit or not. Why would God have put the tree and the fruit there otherwise? The fact that he put it there "in the center of the garden" represents that choice lies at the center of love for the Supreme Being. He perpetually gives us the choice to love Him or not, because how can there be love without choice?

What is the purpose of this world?

The physical world is a place where we can learn and grow. It is a rehabilitation center for those of us who feel we are the most important person in the universe. We choose self-centeredness over loving God. Because this goes against our natural constitution, we are here to learn and find our way back home to our natural spiritual position: One of being in a loving relationship with God.

Subsequently, in this world, we can ignore God, and even deny God's existence if we want. This is how much freedom the Supreme Being gives us with respect to our relationship with Him.

But this physical world is also a place where the Supreme Being has set up numerous lessons for us to learn, according to our desires and level of consciousness. Most of these lessons relate to consequences: "as you sow, so shall you reap."

Yes, we each get back what we put out. This is a universal law because this law was programmed into the physical world in order to create fairness - and to teach us.

Or did we expect that the Supreme Being would toss us out of the spiritual realm with no chance of return? Certainly not. The Supreme Being wants us back.

So He sends His messengers to us to try to canvas us to decide to come back to Him. During that process, He may also impart certain instructions through His representatives, in order to help us grow spiritually and remember Him. 

Some of the rules are specific to the time and circumstance.

Some instructions might be applicable to later generations. But some are not. 

The lesson in Jesus' instruction above about stoning is forgiveness and humility. He is instructing those around him to look at our issues before we sit in judgment of others.

In fact, we have no real ability to sit in judgment of anyone else. Only the Supreme Being has this ability - because only He understands all of the circumstances.

And the Supreme Being is a fair Judge. But He isn't only a good judge: He is also lovable in so many other ways. He is caring, compassionate, fun, humorous, exciting, wonderful and intelligent. This is why Jesus asks us to love the Supreme Being. Because He is lovable:
"‘Love the Lord your God with all your heart and with all your soul and with all your mind.' This is the first and greatest commandment.” (Matthew 22:37-38)