V 29.

By faith they crossed the Red Sea as though it were dry land, whereas the Egyptians, when they attempted the crossing, were drowned.
Exodus 14: 13-29 - the Israelites followed Moses out of Egypt, away from slavery, and through the Red Sea, believing in the promises of God that Moses told them about: that he would lead them home to their own land. Although they were slaves in Egypt, they had no firm proof that where Moses was leading them was going to be any better.  Yet they went.

V 30.

By faith the walls of Jericho fell down after they had been encircled on seven successive days.
Joshua 6.  The Israelites followed what must have seemed like crazy instructions while they had the city of Jericho under siege. resulting in an outstanding victory - God's way, not man's.

V 31.

By faith the prostitute Rahab escaped the doom of the unbelievers, because she had given the spies a kindly welcome.
Joshua 2: 1-21. Rahab sheltered the Israelite spies who had been sent to Jericho ahead of Joshua's armies.  In faith she did as they had instructed to identify herslf and her family and as a result, when Jericho fell, she and her family were spared.  she had no guarantee that the Israelites would keep the word of the spies on her behalf.  She trusted without guarantees. In V 9 & 11,   Rahab told the spies, "I kow the Lord has given you this land....... for the Lord your God is the supreme God of the heavens above and the earth below" (NLT)

V 32 - 38

Need I say more?  Time is too short for me to tell the stories of Gideon, Barak, Samson, and Jephtha, of David and Samuel and the prophets.  Through faith they overthrew kingdoms, established justice, saw God's promises fulfilled. They muzzled ravening lions, quenched the fury of fire, escaped death by the sword.  Their weakness was turned into strength, they grew powerful in war, they put foreign armies to rout. Women received back their dead raised to life.  Others were tortured to death, disdaining release, to win a better resurrection. Others, again, had to face jeers and flogging, even fetters and prison bars. They were stoned, they were sawn in two, they were put to the sword, they went about dressed in skins of sheep or goats, in poverty, distress, and misery. They were too good for a world like this.  They were refugees in deserts and on the hills, hiding in caves and in holes in the ground.

These are examples told in the Old Testament and in the Apocrypha which was written after the period of history covered in the Old Testament.  The Israelite people had suffered all kinds of persecution because of their belief in God and of the promises he had made to Abraham

The writer of Hebrews reminds his readers of the faith of all these people from their nation's past to encourage them when they met challenges to their faith.

V 39 - 40

These also, one and all, are commemorated for their faith; and yet they did not enter the promised inheritance because, with us in mind, God had made a better plan, that only in company with us should they reach their perfection.

Incredible as it may seem, even these people with their great faith did not have access to salvation as we have, because God had not yet put into operation his plan for the salvation of mankind: Jesus had not yet come to walk their land, to die on the crioss and to rise again and defeat death.

V 1.

And what of ourselves?  With all these witnesses around us like a cloud, we must throw off every encumbrance, every sin to which we cling, and run with resolution the race for which we are entered,

Quest Study Bible note, p 1673.  Using the analogy of a race, the writer describes earlier heroes of the faith seated in the stadium, as it were, cheering us on to the finish line.  The testimony of their lives of faith is theri witness.  The record they left behind, like cheers from a grandstand, can encourage us to persevere in our faith.

Just as these witnesses in the past, so can modern-day stories of faith encourage us. And we can encourage each other when we share with others what God has done for us.

When we run this 'marathon race' of  life we are to throw off anything that would hamper our run and which might prevent us from finishing our race well - put aside all distractions that take our focus away from God, get our priorities in order. Running a long race and finishing it well takes perseverance and determination (or resolution).

V 2.

our eyes fixed on Jesus, on whom faith depends from start to finish; Jesus who, for the sake of the joy that lay ahead of him, endured the cross, making light of its disgrace, and has taken his seat at the right hand of the throne of God.

We can persevere when we have someone we love waiting at the finish line to hug and congratulate us.  We have Jesus, who gives us a great example in the way he faithfully 'ran his race' and who is there to encourage and support us along the way.

None of the discouragements we meet are as bad as the difficulties Jesus faced.  And, at least in the so-called 'western world', few of us have to face the difficulties and persecutions the early Christians faced. (Although we know that there are more Christians today suffering persecution for their faith that ever before in the whole of Christian history!)  The faith of the martyrs of the Christian church throughout the centuries in the face of persecution should encourage us when we met discouragements and are tempted to give up on our faith.